Modeling Friction Performance of Drill String Torsional ...downloads.hindawi.com/journals/sv/2017/4051541.pdf · ResearchArticle Modeling Friction Performance of Drill String Torsional

Research ArticleModeling Friction Performance of Drill String TorsionalOscillation Using Dynamic Friction Model

XingmingWang1 Ping Chen1 Zhenhua Rui2 and Fanyao Jin3

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University Chengdu China2Independent Project Analysis Inc Washington DC USA3School of Mechatronic Engineering Southwest Petroleum University Chengdu China

Correspondence should be addressed to Xingming Wang upjzksinacom

Received 2 January 2017 Revised 10 June 2017 Accepted 2 July 2017 Published 14 August 2017

Academic Editor Giorgio Dalpiaz

Copyright copy 2017 Xingming Wang et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Drill string torsional and longitudinal oscillation can significantly reduce axial drag in horizontal drilling An improved theoreticalmodel for the analysis of the frictional force was proposed based on microscopic contact deformation theory and a bristle modelThe established model an improved dynamic friction model established for drill strings in a wellbore was used to determine therelationship of friction force changes and the drill string torsional vibration The model results were in good agreement with theexperimental data verifying the accuracy of the establishedmodelThe analysis of the influence of drillingmud properties indicatedthat there is an approximately linear relationship between the axial friction force and dynamic shear and viscosity The influence ofdrill string torsional oscillation on the axial friction force is discussed The results indicated that the drill string transverse velocityis a prerequisite for reducing axial friction In addition low amplitude of torsional vibration speed can significantly reduce axialfrictionThen increasing the amplitude of transverse vibration speed the effect of axial reduction is not significant In addition byinvolving general field drilling parameters this model can accurately describe the friction behavior and quantitatively predict thefrictional resistance in horizontal drilling

1 Introduction

Directional drilling is a widely used method in the drillingengineering for oil and gas industry The sliding drillingmode is a critical process that drilling string maintainsonly axial sliding movement to keep tool face of downholeassembly (BHA) from rotating (the orientation of tool face ofBHA can control the direction of wellbore) Excessive axialdrag has become a serious problem especially in extended-reach horizontal wells with a motorMWD system Sometechniques are available to reduce drill string drag Rotarysteering systems (RSSs) are configured so that the entire drillrotates continuously with steering capabilities High costshinder the promotion of RSS technology Technology calledldquotorque rockingrdquo or pipe torsional oscillation systems [1ndash4]procedure consists of turning the pipes to the right and thento the left by an amount that avoids interference with the toolface this is depicted in Figure 1 The phenomenon of frictionreduction under the influence of drill string rotation has

been understood and utilized by drilling engineer for yearsHowever the drag reduction mechanism of drill stringsrsquotorsional oscillation is not fully understood

Friction performance is very complex [5] Pohlman andLehfeldt [6] found that longitudinal tangential vibrationsexert a significantly greater influence on the friction forcethan the normal ones Papers argued that [7ndash10] changes ofthe friction force vector under the influence of vibrationscyclic are the cause of the reduction of friction resistance Avariable vector of the relative sliding velocity resulted in theforce being two components one of which is parallel and theother of which is perpendicular to the direction of motionTherefore only a portion of friction acted in the axial direc-tion of the motion Consequently the occurrence friction oftransverse tangential vibration was reduced when the drivingforce was perpendicular to the vibration direction

Experimental investigations [7ndash9] attempted to analyti-cally describe this phenomenon Consistency between ana-lytical and experimental results led to a qualitative fit rather

HindawiShock and VibrationVolume 2017 Article ID 4051541 14 pageshttpsdoiorg10115520174051541

2 Shock and Vibration

Ground surface

Hook load

lsquolsquoTorque rockrsquorsquo

Drilling pipes

Friction force

Gravity

Keep BHA tool face not rotating

Drilling mud

4000sim7000 m

Figure 1 Schematic diagram of ldquotorque rockingrdquo

than quantitative agreement [11] Gutowski and Leus [12]indicated that one of the reasons for the lack of agreementwas that these authors utilized only a simple static CoulombmodelThe computational model established by other papers[12ndash14] based on the Dahl model was in good agreementwith experimental results However the transverse tangentialvibration and sliding motion were separated in the planeand the material properties of the friction pair were thesame The model was not suitable for drill string dynamicsanalysis because the drill string rotary and sliding on thecircular surface and material hardness of the drill pipes androck wellbore were different The model [12] also needed acoefficient of vibration transfer to match the experimentalresults and the coefficient was difficult to determine for drillengineering The model neglected the damp of contact zoneand the viscosity of motion It also did not describe the staticfriction of drill string kinetics however it is important for theanalysis of drill kinematics [1 2]

In this work we presented a dynamic model on thedynamics of the motion of sliding and rotary drill stringsfor perfectly elastic contact in a viscous fluid environmentUnlike Tsai and Tseng [10] Storck et al [8] or Gutowski andLeus [12] the discretized LuGre model was utilized for thefriction model between the drill string and wellbore rock ina well-hole surface The computational model establishingprocess took into account difference in the hardness of thefriction pairmaterial in the downholeThismethodwasmorecomprehensive for describing the friction between the drillstring and wellbore surface

2 Computational Model

21 Surface and Contacts Forms The axial friction force (orcalled drag) in axial direction is a focus problem in drillingengineering Low axial friction can be benefit for drillingDuring rotary drilling or ldquotorque rockingrdquo the motion ofthe drill string is a result of superposition of two motionsThe first of these is drill stringrsquos tangential rotary motion

whereas the second one is sliding motion in the wellborersquosaxial direction

On the macroscopic level the apparent area of wellboresurfaces observed by the naked eye is ldquoroughrdquo [15] Thedrill string surface apparently a smooth surface is stillldquoroughrdquo on amicroscopic levelThemicrocontactmodels [1617] assumed that surfaces are composed of hemisphericallytipped asperities The elastic contact of spheres and halfspaces are governed Hertz equations to compute the loadcontact area and contact pressure acting on a deformedasperity

Considering the real contact between the drill string andthe borehole rock we made the same assumption for thecontact surface This implies that the drill string surface isa slightly rough surface and the wellbore is a severe roughsurface composed of a large number of elastic bristles whichis an abstraction of asperities Due to the roughness andhardness difference between the drill string and wellborerock by surface contact the general elastic bristle in thedynamic frictionmodel should be the bristles on thewellborewhich unlike these models was assumed on the motionbody plane contact The simplified model is shown inFigure 2

22 Basic Assumptions To analyze the real working condi-tions of a drill string in a downhole the following assump-tions are made (1) the bristles on the drill string are rigid (2)the bristles on thewellbore rock are elastic and (3) drill stringrolling friction will not occur

23 Torque and Drag Computational Model Based on theabove assumptions the drill string actual working conditionscan be simplified into the interaction model as shown inFigure 3 The end point of the general bristle connects withthe moving drill string the connecting point will ruptureand rebuild at a different point on the moving body surfacewith the motion of the drill string In the LuGre friction

Shock and Vibration 3

x

y

z

Wellbore

Drill pipe

Drill pipe

Wellbore rock

Contactzone

Contactzone

Torsional oscillation

Rotation

Drill pipe

Wellbore rock

Fd

Figure 2 Modeling of contactrsquos elastic deformation

model [18] the force was determined from the followingequation 997888rarr119865119891 (119905) = 1205901997888rarr119911 (119905) + 1205902119889997888rarr119911 (119905)119889119905 + 997888rarr119865119891 (997888rarr119881119903) (1)

231 Friction Caused by Bristle Deformation It assumed inthe LuGre model that the rate of the elastic strain of ageneral bristle in the contact zone depended on both thetangential rigidity 1205901 of the contact zone as well as the relativevelocity V119903 of the sliding and rotary drill string [18 19] Ageneralized form of this expression was represented by thefollowing equation

= V119903 minus 1003816100381610038161003816V1199031003816100381610038161003816 119911119892 (V119903) (2a)

119892 (V119903) = (119865119888 + (119865119904 minus 119865119888) exp (minus (V119903V119904)2))1205901 (2b)

In the model for further analysis the deformation in thecontact zone formed by the contact of general bristles slidingand the rotary drill string was modeled by a generalizedelastic-damping artificial element 119874119873 which described theaverage behavior of the general bristles (Figure 4)

An elastic-damping deformation 119911 of the contact artificialelement at an optional instant 119905 can be presented in themodel

as the distance of end points119874 and119873 of the elementThe scaleof artificial elements was the micron level the curvature ofthe wellbore surface can be ignored It was determined by thecoordinates of points119874 andM [10] whereM is the projectionof point 119873 on the wellbore surface and can be expressed asfollows

|119911 (119905)| = 100381610038161003816100381610038161003816997888997888997888rarr119874119872100381610038161003816100381610038161003816 119874 (119905) = [0 0] 119872 = [1199090 1199100] (3)

The position ofM at any instant of wellbore is the result ofthe superposition of motion caused by the drill string slidingand tangential motion At consecutive instants the pointM changes its relative position and the elastic deformation119911 also underwent a magnitude and directional change Thedeformation of the elastic bristle was separated into twophases at any interval Δ119905 [10 12]

In the first phase during the previous Δ119905 time step theinstantaneous rotating velocity of the drill string led to themotion of pointsM in the tangential direction In the secondphase the motion of point M was the result of the slidingmotion of the drill string in the axial direction withinΔ119905 timestep

At a consecutive time interval Δ119905 in the first phase ofmotion pointMmoved to the position11987210158401(119905) determined bythe following coordinate

11987210158401 (119905) = [1199091 1199101] = [1199090 1199100 + Δ119909] (4)

At the same time elastic deformation of the bristleprojection vector moved along the path of

997888997888997888997888997888rarr119874119872(119905) to the

path997888997888997888997888997888997888rarr11987411987210158401(119905) The general bristle elastic deformation on the

wellbore surface relied on the contact tangential rigidity 1205901and damping coefficient of the bristle 1205902 The deformationchanged in its magnitude by an increment of Δ119911 which canbe evaluated using (4) In Figure 4 1199111015840(119905+Δ1199052)was the actualmagnitude of elastic deformation of a bristle in the first phaseof motion and can be described by the following relationship

1199111015840 (119905 + Δ1199052 ) = 119911 (119905) + Δ119911 = 119911 (119905) + [[V1199031minus 1003816100381610038161003816V11990311003816100381610038161003816 119911(119865119888 + (119865119904 minus 119865119888) exp (minus (V1199031V119904)2)) 1205901]]Δ119905

(5)

The velocity V1199031 of the relative motion of the generalbristle in the first phase can be determined from the followingexpression

V1199031 =10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158401 (119905)10038161003816100381610038161003816100381610038161003816 minus 100381610038161003816100381610038161003816997888997888997888997888997888rarr119874119872(119905)100381610038161003816100381610038161003816Δ119905 (6)

Knowing the magnitude of elastic deflection 1199111015840(119905 + Δ119905)we can be determine the end point11987210158402 position because the

4 Shock and Vibration

O

z

N(t)

M(t)

x

y

z

Stationary wellbore rock

Tangential velocity of contactsurface Drill pipeDrill pipe

General bristle

Projection point

Axial component

Transverse component

Wellbore rock

Drill pipe

x

y

z

Fd

1

2

Fx

FF Fy

Fg

Fd

FN

of rotary drilling pipes y

zx

zy

x

Torsional oscillation y = ＭＣＨ(t)

Figure 3 Distribution of forces acting on the sliding and torsional oscillation of the drill string

O

M(t)

z(t)

t

x

y

z(t + Δt2)

z(t + 3Δt2)

z(t + 5Δt2)

M2(t + Δt2)

M2(t + 3Δt2)

M2(t + 5Δt2)

z(t + Δt)

z(t + 2Δt)

M(t + Δt)

M(t + 2Δt)M

3(t + 2Δt)

M3(t + Δt)

M3(t)

M1(t)

M1(t + Δt) M

1(t + 2Δt)

y = y(t)

Transverse movement

Figure 4 Changes in a general bristles deformation at consecutive phases of sliding and torsional oscillation of the drill string

Shock and Vibration 5

direction of 1199111015840(119905 + Δ119905) was along vector997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402(119905 + Δ119905) The

coordinates were described as follows

11987210158402 (119905 + Δ119905) = [1199092 1199102] = 10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402 (119905 + Δ119905)10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161199111015840 (119905 + Δ119905)1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158401 (119905)10038161003816100381610038161003816100381610038161003816

= [1199092 1199102] 100381610038161003816100381610038161199111015840 (119905 + Δ119905)1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158401 (119905)10038161003816100381610038161003816100381610038161003816 (7)

The angle between the elastic deformation997888997888997888997888997888997888997888997888rarr1199111015840(119905 + Δ119905) and

wellbore axial direction can be determined according to theimposed equation

120572 = acrcos(997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402 (119905 + Δ119905) sdot 997888rarr119890110038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402 (119905 + Δ119905)10038161003816100381610038161003816100381610038161003816 ) (8)

In the second phase during the following Δ119905 time stepdrill string sliding led to themotion of points11987210158402(119905+Δ119905) in thelongitudinal direction After the expiry of Δ119905 the drill stringsliding displacement is Δ119909 This displacement related to the

distance of1198721015840211987210158403(119905)The value of997888997888997888997888997888997888997888997888rarr1199111015840(119905 + Δ119905) corresponded to

themagnitude of elastic deflection of the bristle after the timeinterval Δ119905 This can be described as follows

119911 (119905 + Δ119905) = 1199111015840 (119905 + Δ119905) + Δ1199111015840 = 1199111015840 (119905 + Δ119905) + [[V1199032minus 1003816100381610038161003816V11990321003816100381610038161003816 119911(119865119888 + (119865119904 minus 119865119888) exp (minus (V1199032V119904)2)) 1205901]]Δ119905

(9)

Velocity V1199032 approximately was equal to the averagevelocity of point11987210158402(119905 + Δ119905) along the straight line 11987411987210158403(119905)The value can be determined from the following equation

V1199031 =10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158403 (119905)10038161003816100381610038161003816100381610038161003816 minus 10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402 (119905 + Δ119905)10038161003816100381610038161003816100381610038161003816Δ1199052 (10)

where997888997888997888997888997888997888rarr11987411987210158403(119905) = 997888997888997888997888997888997888997888997888997888997888997888997888997888rarr11987411987210158402(119905 + Δ1199052) + Δ119909997888rarr1198901 The magnitude of997888997888997888997888997888997888997888rarr119911(119905 + Δ119905)was proportional to |997888997888997888997888997888997888rarr11987411987210158403(119905)|11987210158403(119905) that was119872(119905+Δ119905) was determined from the following equation

11987210158403 (119905) = 119872 (119905 + Δ119905) = [1199093 1199103] = 10038161003816100381610038161003816100381610038161003816997888997888997888997888rarr1198741198721015840310038161003816100381610038161003816100381610038161003816 |119911 (119905 + Δ119905)|10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158403 (119905)10038161003816100381610038161003816100381610038161003816= [1199093 1199103] |119911 (119905 + Δ119905)|10038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158403 (119905)10038161003816100381610038161003816100381610038161003816 (11)

Angle 120573 between997888997888997888997888997888997888rarr11987411987210158403(119905) and the axial direction can be

determined by the following expression

120573 = acrcos(997888997888997888997888997888997888rarr11987411987210158403 (119905) sdot 997888rarr119890110038161003816100381610038161003816100381610038161003816997888997888997888997888997888997888rarr11987411987210158403 (119905)10038161003816100381610038161003816100381610038161003816 ) (12)

Knowing the magnitude and direction of elastic defor-mation z at any time interval Δ119905 the instantaneous values offriction force 119891119889 and 119898119889 were determined at this instant byutilizing the LuGre model119891119889 = [1205901119911 (119905 + Δ119905) + 1205902 (119905 + Δ119905)] cos120573 (13)

The torque caused by bristle deformationwas determinedby the following expression119898119889 = 1198770119891119910 = 1198770 [1205901119911 (119905 + Δ119905) + 1205902 (119905 + Δ119905)] sin120573 (14)

232 Friction Caused by Viscous Fluid 997888rarr119865119891(997888rarr119881119903) was themotion viscous force of the drill string in the drillingmud and997888rarr119881119903was the drill-stringmotionmacroscope velocity vector notthe elastic deformation of the bristle on the wellbore [20]Hence the damping coefficient was described in Li (2008)as the following equation

119891V = minus2120587V( 1198770120591radicV2 + (1198770120596)2 + 120583ln (11986311990821198770))119889119909

119898V = minus212058711987730120596( 120591radicV2 + (1198770120596)2 + 2120583119863119908 minus 21198770)119889119909(15)

233 Average Magnitude of Torque and Drag The averagemagnitude force 119865119891 in the axial direction of the wellbore andduring a period of time relates to themagnitude of the frictionforce in this direction and was essential for initiating andsustaining the drill stringmotion It was determined from thefollowing relationship respectively

119865119891 = 1119899 sum 1003816100381610038161003816119891119889 (119905119899) + 119891V (119905119899)1003816100381610038161003816 (16)

The average magnitude torque 119872119891 during a period ofmotion of drill string can be described as follows

119872119891 = 1119899 sum 1003816100381610038161003816119898119889 (119905119899) + 119898V (119905119899)1003816100381610038161003816 (17)

Therefore the average friction drag due to bristle defor-mation and viscose fluid can be noted respectively

119891119889 = 1119899 sum 1003816100381610038161003816119891119889 (119905119899)1003816100381610038161003816 (18)

119891V = 1119899 sum 1003816100381610038161003816119891V (119905119899)1003816100381610038161003816 (19)

6 Shock and Vibration

The average friction torque caused by bristle deformationand viscose fluid can be determined from the followingrelationship respectively119898119889 = 1119899 sum 1003816100381610038161003816119898119889 (119905119899)1003816100381610038161003816 (20)

119898V = 1119899 sum 1003816100381610038161003816119898V (119905119899)1003816100381610038161003816 (21)

3 Model Solution and Model Verification

31 Model Calculation Program Based on the aforemen-tioned calculation model the solving procedure step ofnovel dynamic friction model was presented in Figure 5 Theprocedure included two parts (I and II) Part I presentedthe bristle elasticity and damping force calculation processon the microlevel including two half-time steps Part IIpresented a drilling fluid viscous force at the macrolevelThe macrovelocity vector was the combined longitudinaldirection and tangential direction velocity

32 Model Verification To assess the validity of the estab-lished model experimental data and parameter mentionedin paper [12] were adopted to verify established model Theparameters [12] included a frequency of 119891 = 3000Hz a nor-mal pressure of119901119899 = 0022Nmm2 an area of119860 = 1200mm2a coefficient of contact rigidity in tangential direction of 1205901 =6729N120583m a coefficient of contact damping in tangentialdirection of 1205902 = 1 times 10minus3N(120583ms) a coefficient of staticfriction of 120583119862 = 0106 and a coefficient of static friction of120583119878 = 0193 There were no fluid effects on the moving bodyand the coefficient of viscosity dampingwas1205903 = 0N(120583ms)

The experiment presented in the paper was investigatedin terms of the influence of tangential contact vibration onthe friction force The aforementioned model was adopted tocalculate the change in the friction force with the dimension-less velocity and to compare it with the experimental results(Figure 6)The calculated results are in reasonable agreementwith the experimental dataThe largest error is 3017 and theaverage error is 921

The model described in the paper by Gutowski and Leus[12] is also in good agreement with the experimental resultsHowever the influence of a coefficient of vibration transfer inthe model [12] is greater than body relative velocity in someconditions It is also extremely difficult to determine in drillengineering adopting the model described by Gutowski andLeus [12]

4 Discussion and Analysis

41 Simulation Parameters According to the experimentalresults the established model can accurately predict thefriction from tangential vibration coupled with the slid-ing motion Therefore this model can also describe drillstring torsional vibration with sliding in a downhole from atheoretical perspective Drill pipes in a horizontal wellborewere adopted to analyze axial friction reduction mechanismcaused by drill pipe torsional oscillation using general fielddrilling parameters

Table 1 Simulation parameters [12 26ndash28]

Number Parameterunit Value1 Coulomb friction coefficient 0212 Static friction coefficient 0253 Friction Stiffness coefficient(Nmm) 504 Friction Damping coefficient(N(mms)) 03165 Stribeck velocity(120583ms) 1906 Length of drill pipem 107 Outer diameter of drill pipem 01278 Inner diameter of drill pipem 010869 Wellbore diameterm 0215610 Dynamic shearPa 1511 ViscosityPasdots 00312 Density of drill pipe(kgm3) 785013 Density of drill mud(kgm3) 220014 Volume rate(Ls) 30

Static and kinetic friction coefficients are fundamentalparameters for friction force simulation of drilling string Inthe paper [21] static friction coefficient is equal to 025 andkinetic friction coefficient is equal to 021 Simulation results[21] are in good agreement with the field measured data

Wang et al [22] obtained friction stiffness coefficientbetween steel and rock at different frequencies in the experi-mental environmentThe friction stiffness coefficient is equalto 50Nmm This parameter has good consistence withexperimental data [22]

However there are rare reports about friction dampingcoefficient between steel and rock obtained through exper-iment research The parameter can be 0316Nsdotsmm [18]0214Nsdotsmm [14] and 05Nsdotsmm [23] Mehmood et al(2012) and Yu et al [24] obtained sensitivity analysis results ofparameters in the LuGre friction model The results showedthat coefficient 1205902 is less sensitive as compared to119865119888 and119865119904 Inthis paper damping coefficient 1205902 was equal to 0316Nsdotsmm[18]

Stribeck velocity is also less sensitive than 119865119888 and 119865119904according to Mehmood et al (2012) and Yu et al [24] Therock is multiscale porous medium [25] Giorgio and Scerrato[26] give values of the Stribeck velocity for a multiporousrock medium Wang et al [27] provided parameters used incalculating mud damping effects

Basic simulation parameters were assumed to analyze thedrill string axial friction performance affected by rotation andtorsional vibration as shown in Table 1

42 Parameter Sensitivity Study Tsai and Tseng [10] andGutowski and Leus [12] described a discrete bristle defor-mation process based on the Dahl model This sectionnumerically exploited the influence of two parameters in theLuGremodel that the Dahlmodel does not adopt Piatkowski[29] analyzed the properties between the Dahl and LuGredynamic frictionmodels in depthThis sectionmainly studiesthe following contents (1) the importance of taking theStribeck velocity of the LuGre model into account and (2)the relevance of damping coefficient 1205901 in the longitudinalfriction force

Shock and Vibration 7

Output the result

Calculation friction force relates to bristle deformation

Calculation drilling mud viscous force

Calculation drill string friction force

Part-I Part-II

Yes

No

Intial parameters

No Yes

Input basic parameters [1 2 3 2 Vs Fc Fs]

n = 1

Read basic parameters at(n minus 1)Δt

string tangential displacement ΔyCalculation previous Δt2 drill

microscope tangential velocityCalculation previous Δt2 drill string

Calculation coordinates of visual point M

1

Calculation coordinates of visual point M

3

bristle vector deformation rateCalculation previous Δt2 elastic

Calculation coordinate of visual point M

2

string axial displacementCalculation following Δt2 drill

string microscope axial velocityCalculation following Δt2 drill

bristle vector deformation rateCalculation following Δt2 elastic

Calculation coordinates of actual point M(t + Δt)

n = n + 1 nΔt ⩽ ＮＣＧ

Figure 5 Present model solution flow chart

8 Shock and Vibration

0 02 04 06 08 1 12 14

0

02

04

06

08

1

Experimental (Gutowski and Leus 2015)Model

minus02

da

FfxF

C

Figure 6 Comparison between the numerical simulation andexperimental results

421 Stribeck Velocity V119904 Study Maidla et al [1 2] describeda force that was applied to a stationary drill string in adownhole and slowly increased until the drill string slidesThe sliding resistance experienced two stages static frictionand dynamic friction The static friction was approximately25 greater than the dynamic frictionMeanwhile the LuGremodel continues at any instant and can describe dynamic andstatic characteristics without a velocity piecewise functionThis model can also analyze the transition process from staticand dynamic friction which the Dahl model cannot

The effect of the amplitude of the Stribeck velocityis depicted in Figure 7 which varied from 100120583ms to300 120583msThe axial slide velocity was 27778120583msThe rate ofpenetration (ROP) was equivalent to 1mh It was a commonoperation parameter in the horizontal well drilling field

The simulation result of friction ratio was extremely lowusing drilling field operation parameters However the axialfriction ratio held steady with varied Stribeck velocity at thesame vibration amplitude It indicated that the axial frictionratio was low sensitive to the Stribeck velocity using thedrilling operation parameter The result of Yu et al was alsoconfirmed [24]

422 Damping Coefficient 1205902 Study Thedamping coefficient1205902 is a microdamping coefficient in the generalized bristlemodel Hence the LuGre model is applied prior to the Dahlmodel to describe and predict the general bristle deflectionprocess According to the description of the LuGre model(De Wit and Carlos Canudas 1995) the damping coefficientof the average behavior of bristle deflection is relative toa parameterization of 119892(V119903) which has been proposed todescribe the Stribeck effect in (2a) and (2b) This sectiondiscusses how varied 1205902 affects the longitudinal friction force

The numerical results are shown in Figure 8The longitu-dinal direction velocity was equal to 1mh of ROP As increas-ing of vibration amplitude the axial friction ratio rapidly

2 4 6 8 100

001

002

003

004

005

006

Ωa (rpm)

FfxF

c

Vs = 100 ＧＭ

Vs = 120 ＧＭ

Vs = 140 ＧＭ

Vs = 160 ＧＭ

Vs = 180 ＧＭ

Vs = 200 ＧＭ

Vs = 220 ＧＭ

Vs = 240 ＧＭ

Vs = 260 ＧＭ

Vs = 280 ＧＭ

Vs = 300 ＧＭ

Figure 7 Influence of the Stribeck velocity on the change in friction

2 4 6 8 100

001

002

003

004

005

006

007

Ωa (rpm)

FfxF

c

2 = 100 Nmiddotsm2 = 200 Nmiddotsm2 = 300 Nmiddotsm

2 = 400 Nmiddotsm2 = 500 Nmiddotsm

Figure 8 Influence of the damp coefficient of general bristles on thechange in friction

decreased However the greater friction damp coefficientwas related to higher axial friction ratio at the same velocityamplitude of torsional vibration The growth of friction ratiowas relatedly low with increasing of damp coefficient Itsuggested that damp coefficient of bristle deformation wasmore sensitive than Stribeck velocity However it was littleeffect of damp coefficient on axial friction as well

Shock and Vibration 9

0 5 10 15 20 25 302

4

6

8

10

12

14

16

18

Aver

age a

xial

visc

ous f

orce

(N)

Ωa = 10 rpmΩa = 12 rpmΩa = 14 rpmΩa = 16 rpmΩa = 18 rpm

Ωa = 22 rpmΩa = 24 rpmΩa = 26 rpmΩa = 28 rpmΩa = 30 rpm

Ωa = 20 rpm

(Pa)

Figure 9 Influence of dynamic shear of drilling mud on the changein axial viscous force

43 Viscous Friction of Drilling Mud

431 Effect of Mud Dynamic Shear Parametric studies wererun to explore the relationship between dynamic shear andaxial friction resistance for drill pipes as shown in Figure 9ROP was equal to 7mh The axial force slowly rises withincreasing of the value of dynamic shear The relationshipbetween the axial force and dynamic shear was approximatelylinear within the drill string torsional oscillation amplitudesof 10 rpmand 30 rpmWhen the dynamic shear is small it waslittle distinction of average axial viscous force that affecteddifferent torsional vibration amplitude Value of average axialviscous force increased with dynamics shear The greateraverage axial viscous force was with lower torsional vibrationamplitude

432 Effect of Frequency This section discussed influence oftorsional vibration amplitude of average axial viscous forceThe ROP was equal to 7mh The range of torsional oscilla-tion amplitude was between 10 rpm and 30 rpm while therewere common parameters in the drilling fluid Average axialviscous force decreased with torsional oscillation amplitudeincreasing (Figure 10) Curve of 1Hz was slightly higher thancurve of 1HzHowever curve of 10Hzwas remarkably greaterthan curve of 1Hz

433 Effect of Viscosity Axial viscous force was also affectedby viscosity of drilling mud As shown in Figure 11 theviscous force was increasing with the value of viscosityof drilling fluid However the whole descending of axialforce was remarkable at first and tiny at last with viscosityincreasing In the same as above the lower torsional vibrationamplitude led to greater axial viscous force It was linear

10 15 20 25 306

65

7

75

8

85

9

95

10

105

Aver

age a

xial

visc

ous f

orce

(N)

Ωa (rpm)

f = 01 Hzf = 1 Hzf = 10 Hz

Figure 10 Influence of frequency of torsional oscillation on the axialviscous force

Ωa = 10 ＬＪＧ

Ωa = 12 ＬＪＧ

Ωa = 14 ＬＪＧ

Ωa = 16 ＬＪＧ

Ωa = 18 ＬＪＧ

Ωa = 22 ＬＪＧ

Ωa = 24 ＬＪＧ

Ωa = 26 ＬＪＧ

Ωa = 28 ＬＪＧ

Ωa = 30 ＬＪＧ

Ωa = 20 ＬＪＧ

001 002 003 004 005 0064

5

6

7

8

9

10

11

12

13

14

Aver

age a

xial

visc

ous f

orce

(N)

(Pamiddots)

Figure 11 Influence of viscosity of drilling mud on the change inaxial viscous force

relationship between average axial viscous force and viscosityof fluid Therefore it can be effectively reducing axial viscousfriction force by enhancing velocity amplitude of torsionalvibration

434 Axial Viscous Friction Force Reduction To analyzeviscous friction force reduction axial viscous friction forceand viscous friction torque were compared in time domainAs shown in Figure 12 the viscous friction torque was

10 Shock and Vibration

4 42 44 46 48 5

Time (s)

0

10

20

30

40

50

60

70

Aver

age a

xial

visc

ous f

orce

(N)

minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

Aver

age a

xial

visc

ous t

orqu

e (Nmiddotm

)

Figure 12 Viscous force and torque of drilling pipes in time domain

symmetric distribution about zeros When absolute value ofviscous friction torque was increasing absolute value of axialviscous friction force would be decreasing When the torquewas approaching zero the axial viscous friction became thegreatest Therefore axial viscous friction force reductionwas due to torsional motion of drill string decomposed ofsome axial viscous friction force This axial force reductionmechanism was benefit for drilling engineering

44 Friction of Bristle Deformation

441 Effect of Torsional Vibration Frequency The effect ofthe frequency of torsional oscillation on the axial drag forcewas discussed in this section According to the commonfrequency and amplitude range of torque rocking drilling01 Hz 1 Hz and 10Hz were selected to analyze the frictionreduction in the longitudinal direction The drill string slidevelocity was equal to 00025ms corresponding to an ROP of9mh Other simulation parameters were listed in Table 1

As shown in Figure 12 the force ratio curves of 01 Hz1 Hz and 10Hz were decreased with torsional vibrationamplitude increased The axial sliding friction force overalldecreased as the frequency of torsional vibration increasedfrom 01Hz to 1Hz When the frequency of torsional vibra-tion changed from 1Hz to 10Hz the axial friction overallincreased Thus these were an optimum frequency that theaxial friction was the lowest

442 Effect of ROP and Torsional Vibration Amplitude Inaddition to studying the interesting drag reduction of tor-sional oscillation drilling an analysis was run to explore therelationship between ROP and the longitudinal friction forceas shown in Figure 14 The frequency of torsional vibrationwas 5Hz ROPwas between 1mh and 9mh with 2mh stepThe amplitude of torsional oscillation was between 10 rpmand 30 rpm with 2 rpm step Other simulation parameterswere listed in Table 1

The ratio of the axial and Coulomb friction decreased asthe torsional oscillation amplitude increased The reductionrate was remarkable in the region that the amplitude wasbelow 20 rpm and the downward rate of curves decreased outof that regionThe increasing ROP led to a larger axial friction

10 12 14 16 18 20 22 24 26 28 30002

004

006

008

01

012

014

FfxF

C

Ωa (rpm)

f = 01 Hzf = 1 Hzf = 10 Hz

Figure 13 Influence of frequency of torsional oscillation on the axialfriction due to bristle deformation

10 12 14 16 18 20 22 24 26 28 300

005

01

015

02

025

03

035

04

045

Ωa (rpm)

FfxF

c

d = 1 mhd = 3 mh

d = 7 mhd = 9 mh

d = 5 mh

Figure 14 Influence of amplitude of drill string torsional oscillationon the change in axial friction

component ratio The higher axial velocity component ofthe drill string contributed to a longer length of the bristleprojected in the axial direction according the establishedmodel (Figure 13)

The curve for the transverse friction force and transversevibration velocity formed a loop that described hysteresisfriction The relationship between the axial friction forceand relatively motion velocity had hysteretic properties asdepicted in Figure 15 There is less difference of loops with1mh 3mh 5mh 7mh and 9mh The major differencewas between 01ms and 015ms This was at the balanceposition The deformation directions of bristle were reversed

Shock and Vibration 11

d = 1 mhd = 3 mh

d = 7 mhd = 9 mh

d = 5 mh

0 005 01 015

0

50

100

150

200

minus015 minus01 minus005minus200

minus150

minus100

minus50

Vy (ms)

Fy

(N)

Figure 15 Influence of different amplitudes of torsional oscillationon transverse friction

0 005 01 0150

10

20

30

40

50

60

70

Fd

(N)

minus015 minus01 minus005

Vy (ms)

d = 1 mhd = 3 mhd = 5 mh

d = 7 mhd = 9 mh

Figure 16 Loop of the axial force of the drill string and relativemotion velocity

in the 119910 direction The greater drag velocity led to a largerhysteresis loop The distinction of loops was tiny to thedrilling engineering

The relationship of axial direction friction and velocitywas shown in Figure 16 The curve of each drag velocityalso formed a loop The amplitude of the loop and max-imum axial friction resistance increased as the amplitudeof torsional oscillation velocity increased At the maximumvelocity the tangential force rapidly increased and formedpeak Out of range of the maximum velocity the axial forcerapidly decreased and became steadyTherewere greater peakamplitude and greater steady value with greater drag velocity

minus50 0 50 100 150 200 250 300minus100

y (m)

minus4000

minus3000

minus2000

minus1000

0

1000

2000

3000

4000

x(

m)

d = 1 mhd = 3 mhd = 5 mh

d = 7 mhd = 9 mh

Figure 17 Trajectory of general bristle end point projection

Tiny distinction of tangential force led to larger difference ofaxial friction in the range of drilling engineering parameters

443 Trajectory of the Bristle Deformation Projection Thetrajectory of the bristle projection point was depicted inFigure 17 The bristle deformation directly influences theforce exerted on the moving drill string As Figure 17 showsROP was between 1mh and 9mh with 2mh step and thegeneral bristle end point project motion trajectory was influ-enced by different velocity amplitudes of torsional oscillation

Shape of trajectory liked a symbol of infinite Howeverthe trajectory loops of different drag velocities were symmet-ric with respect to 119909 = 0Therewere intersection of trajectorynear the range of 119909 = 0 The number of intersections oftrajectory was less with low drag velocityWhen drag velocitywas above 5mh there were three times of intersection

The trajectory loop was flat and narrow when the dragvelocity was lowHowever the loop becamewider and curvedwith increase of drag velocity The up and down ends ofloop were toward the back It was because stiffness coefficientof bristle deformation was greater than value of Gutowskiand Leus [12] When drag velocity was low bristle can easilydeform in the small area As drag velocity became great thebristle cannot deform in the larger range Therefore loopwith greater ROP was bended to back Meanwhile the loopsbecame wider

Projection position of bristle in 119910 direction with timewas presented in Figure 18 The trajectories were symmetrywith respect to x axial The curves of different drag velocitywere almost superposition However the time and positionof reversing point with low drag velocity was earlier higherthan ones of greater drag velocityTherefore the drag velocitymainly influenced peak position of the trajectory in 119910direction

The amplitude of trajectory was lower than amplitudeof torsional vibration It was because the connection point

12 Shock and Vibration

96 965 97 975 98 985 99 995 10Time (s)

0

1000

2000

3000

4000

5000

Torsional vibration

d = 1 mhd = 3 mhd = 5 mh

d = 7 mhd = 9 mh

minus1000

minus2000

minus3000

minus4000

minus5000

y(

m)

Figure 18 Trajectory of bristle projection and drilling pipe torsionaloscillation in time domain

between bristle and drilling pipe was ruptured and rebuiltMeanwhile there was obvious hysteresis between trajectoryof projection point and trajectory of torsional oscillation Inthe area that trajectory of torsional vibration intersected withtrajectory of projection point there was obvious difference oftrajectory with different drag velocity

45 Relationship of Torque and Drag Figure 19 presentedfriction force in axial direction caused by bristle deformationand viscous fluid in time domain The viscous friction wasfollowed with torsional velocityThe viscous friction decreasewith value of torsional velocity became greater Howeverfriction force due to bristle deformation fell behind by variedtorsional velocity The pattern of two friction forces wasmutually consistent The levels of two friction forces wereclose to each other

Figure 20 presented friction torque in axial directioncaused by bristle deformation and viscous fluid in timedomain There was also hysteresis between the varied torquecaused by bristle deformation and drilling pipe torsionalvelocity The value of torque due to bristle deformationincreased with the value of friction decrease There wassimilar pattern between axial friction force and frictiontorque caused by bristle deformation The torque of viscousfluid was obviously lower than ones of bristle deformation

5 Conclusions

Given the microscope complex and field-oriented nature ofthe current rotation and torsional oscillation drill string axialfriction resistance the goal of this paper was to present asimple dynamic friction model based on the discrete LuGremodel for the analysis of tribological effects in horizontalwell drilling This model was established on the basis of theaverage deflection of the general bristle model and considersthe viscosity effect of mud It is superior for describing the

16 165 17 175 18 185 19 195 2Time (s)

0

20

40

60

80

Fric

tion

forc

e (N

)

0

01

02

Tors

iona

l velo

city

(ms

)

Brittles deformationViscous fluidTorsional velocity

minus02

minus01

Figure 19 Friction force of bristle deformation and viscous fluid intime domain

16 165 17 175 18 185 19 195 2Time (s)

0

10

20

0

01

02

Tors

iona

l velo

city

(ms

)

Brittles deformationViscous fluidTorsional velocity

minus20

minus10

minus02

minus01Fric

tion

torq

ue (N

middotm)

Figure 20 Friction torque of bristle deformation and viscous fluidin time domain

tribological behavior between the drill string and the rockof the wellbore A computational program was developed tosolve the present model which was utilized to predict instan-taneous general bristle deformation and frictional resistanceat the contact surface

The established model was verified using experimentaldata without adopting a coefficient of vibration transfer Thecomputational results were consistent with the experimentalresults The model can be applied to analyze the frictionalresistance of the drill string and wellbore The parametersensitivity studies were used to evaluate the effect of themagnitude of the Stribeck velocity and general bristle defor-mation dampThe results indicated that Stribeck velocity anddamp of bristle deformation were not sensitive to frictionusing the drilling operation parameter

Shock and Vibration 13

Drilling parameters of general field were adopted toanalyze drill string axial and circumferential friction torqueusing the presentmodelThe amplitude of dynamic shear andviscosity of drilling mud was positively correlated with thedrill string axial friction resistance

The drag of drilling pipe also decreased with increaseof torsional vibration amplitude There was an optimalfrequency thatminimizes axial friction in the range of drillingparameters of general field The axial friction would increasewith increase of ROP There was the order of magnitudesthat the value of axial friction caused by bristle deformationand viscous fluid The torque caused by bristle deformationwas greater than ones of viscous fluid in range of drillingparameters of general field

We introduce this concept into drilling engineering tocapture the reality of drill string torque and drag We cancombine the model of conventional drill string mechanicswith the discrete LuGre model to forecast proper technologyin drilling horizontal wells

Nomenclature119865119891 Average of friction torque of bristle deformation andviscous fluid N119872119891 Average of friction torque of bristle deformation andviscous fluid N997888rarr1198901 A unit vector of axial direction of drill string119891119889 Average of friction force of bristle deformation N119891V Average of friction force of viscous fluid N119898119889 Average of friction torque of bristle deformation N119898V Average of friction torque of viscous fluid N119863119908 Diameter of wellbore mm119865119865 Dynamic friction force N119865119888 Coulomb friction force N119865119891119909 Axial direction component of dynamic friction forceN119865119891119910 Tangential direction component of dynamic frictionforce N119865119904 Static friction force N1198770 Outer diameter of drill string mm119891119889 Friction force of bristle deformation N119891V Friction force of viscous fluid N119898119889 Friction torque of bristle deformation N119898V Friction torque of viscous fluid N

V119903 Velocity of relative motion drill string msV1199031 Virtual relative velocity of motion drill string in

previous half of time step 120583msV1199032 Virtual relative velocity of motion drill string in

following half of time step 120583msV119904 Stribeck velocity 120583msV119909 Axial direction velocity component of motion drill

string msV119910 Instantaneous tangential direction velocity

component of motion drill string ms1199091 119909 coordinate of end point of bristle projection11987210158401 120583m1199092 119909 coordinate of end point of bristle projection11987210158402 120583m1199093 119909 coordinate of end point of bristle projection11987210158403 120583m1199101 119910 coordinate of end point of bristle projection11987210158401 120583m

1199102 119910 coordinate of end point of bristle projection11987210158402 120583m1199103 119910 coordinate of end point of bristle projection11987210158403 120583m1205901 Tangential stiffness of general bristles N120583m1205902 Damp coefficient of general bristles N(120583ms)1205903 Damp coefficient of mud viscous friction N(ms)119863119908 The well-hole inner diameter m119889119909 The length of drilling pipes m1198770 The outer radius of drilling pipes mV The axial velocity of drilling pipes considering fluid

consist of V119909 and mean velocity of fluid ms120572 Angle between virtual elastic deformation vector ofgeneral bristle and axial direction rad120573 Angle between elastic deformation vector of generalbristle and axial direction rad120582 Coefficient of drill string eccentric dimensionless120583 Viscosity of drilling mud Pasdots120591 Dynamic shear of drill string MPa120596 The rotating angular velocity of drilling pipe rads119872 End point of bristle projection119899 Number of time step in one second dimensionless119909 119909 coordinate of end point of bristle projectionM 120583m119910 119910 coordinate of end point of bristle projectionM 120583m119911 Elastic deformation of general bristles 120583m1199111015840 Virtual elastic deformation of general bristles in thecalculation time step 120583mΔ119905 Time step 1119890 minus 6 sΔ119909 Axial direction relative displacement of motion drillstring in one time step 120583mΔ119910 Axial direction relative displacement of motion drillstring in one time step 120583mΩ Amplitude of torsional oscillation rpm119881119903 Macroscope velocity relative to drilling fluid ms

Additional Points

Highlights An improved discrete LuGre model and methodfor describing and predicting the friction between a drillstring and wellbore rock was established for given downholeconditions The influence of mud properties and torsionaloscillation parameters on the axial and transverse frictionresistance was discussed based on the established model

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research was sponsored by the National NaturalScience Foundation of China (Grant no 51274171) theSichuan Province Science amp Technology Program (Grantno 2015SZ0003) and the National Science and TechnologyMajor Project of China (Grant no 2016ZX05022-01)

References

[1] E Maidla and M Haci ldquoUnderstanding Torque The Keyto Slide-Drilling Directional Wellsrdquo in Proceedings of theIADCSPE Drilling Conference Society of Petroleum EngineersDallas Tex USA 2004

14 Shock and Vibration

[2] E Maidla M Haci S Jones M Cluchey M Alexander andT Warren ldquoField proof of the new sliding technology fordirectional drillingrdquo in Proceedings of the 2005 SPEIADCDrilling Conference - Drilling Technology Back to Basics pp723ndash730 February 2005

[3] E Maidla M Haci and D Wright ldquoCase history summaryHorizontal drilling performance improvement due to torquerocking on 800 horizontal land wells drilled for unconventionalgas resourcesrdquo in Proceedings of the SPE Annual TechnicalConference and Exhibition 2009 ATCE 2009 pp 195ndash206October 2009

[4] C Gillan S Boone G Kostiuk C Schlembach J Pinto andMLeBlanc ldquoApplying precision drill pipe rotation and oscillationto slide drilling problemsrdquo in Proceedings of the SPEIADCDrilling Conference and Exhibition 2009 pp 53ndash65March 2009

[5] M Urbakh J Klafter D Gourdon and J Israelachvill ldquoThenonlinear nature of frictionrdquoNature vol 430 no 6999 pp 525ndash528 2004

[6] R Pohlman and E Lehfeldt ldquoInfluence of ultrasonic vibrationonmetallic frictionrdquoUltrasonics vol 4 no 4 pp 178ndash185 1966

[7] S Matunaga and J OnodA ldquoA novel method of frictionforce reduction by vibration and its application to gravitycompensationrdquo in Proceedings of the 33rd Structures StructuralDynamics and Materials Conference Dallas Tex USA 1992

[8] H Storck W Littmann J Wallaschek and M Mracek ldquoTheeffect of friction reduction in presence of ultrasonic vibrationsand its relevance to travelling wave ultrasonic motorsrdquo Ultra-sonics vol 40 no 1-8 pp 379ndash383 2002

[9] V C Kumar and IM Hutchings ldquoReduction of the sliding fric-tion of metals by the application of longitudinal or transverseultrasonic vibrationrdquo Tribology International vol 37 no 10 pp833ndash840 2004

[10] C C Tsai and C H Tseng ldquoThe effect of friction reductionin the presence of in-plane vibrationsrdquo Archive of AppliedMechanics vol 75 no 2-3 pp 164ndash176 2006

[11] P Gutowski and M Leus ldquoThe effect of longitudinal tangentialvibrations on friction and driving forces in sliding motionrdquoTribology International vol 55 pp 108ndash118 2012

[12] P Gutowski and M Leus ldquoComputational model for frictionforce estimation in sliding motion at transverse tangentialvibrations of elastic contact supportrdquo Tribology Internationalvol 90 pp 455ndash462 2015

[13] X Wang P Chen and T Ma ldquoa Modeling and experimentalinvestigations on the drag reduction performance of an axialoscillation toolrdquo Journal of Natural Gas Science Engineering pp39ndash118 2017

[14] A Mehmood S Laghrouche M El Bagdouri and F S AhmedldquoSensitivity analysis of lugre friction model for pneumaticactuator controlrdquo in Proceedings of the 2010 IEEE Vehicle Powerand Propulsion Conference VPPC 2010 September 2010

[15] P S M Dougherty R Pudjoprawoto and C Fred HiggsldquoBit cutter-on-rock tribometry Analyzing friction and rate-of-penetration for deep well drilling substratesrdquo TribologyInternational vol 77 pp 178ndash185 2014

[16] J A Greenwood and J B P Williamson ldquoContact of nominallyflat surfacesrdquo Proceedings of the Royal Society of London AMathematical Physical and Engineering Sciences vol 295 no1442 pp 300ndash319 1966

[17] A Majumdar and B Bhushan ldquoFractal model of elastic-plasticcontact between rough surfacesrdquo Journal of Tribology vol 113no 1 pp 1ndash11 1991

[18] C Canudas de Wit H Olsson K J Astrom and P LischinskyldquoA new model for control of systems with frictionrdquo IEEETransactions on Automatic Control vol 40 no 3 pp 419ndash4251995

[19] H Olsson K J Astrom C Canudas De Wit M Gafvert andP Lischinsky ldquoFriction Models and Friction CompensationrdquoEuropean Journal of Control vol 4 no 3 pp 176ndash195 1998

[20] S A Mirhaj ldquoEvaluation of Shear Forces and Stream-ThrustForces in Torque and Drag Analysisrdquo in Proceedings of the SPEAsia Pacific Oil and Gas Conference and Exhibition JakartaIndonesia 2001

[21] E Cayeux H J Skadsem B Daireaux and R HolandldquoChallenges and Solutions to the Correct Interpretation ofDrilling Friction Testsrdquo in Proceedings of the SPEIADCDrillingConference and Exhibition The Hague The Netherlands 2017

[22] P Wang H Ni R Wang Z Li and Y Wang ldquoExperimentalinvestigation of the effect of in-plane vibrations on friction fordifferentmaterialsrdquoTribology International vol 99 pp 237ndash2472016

[23] M R Kermani R V Patel and M Moallem ldquoFriction identi-fication in robotic manipulators case studiesrdquo in Proceedings of2005 IEEE Conference on Control Applications 2005 CCA 2005pp 1170ndash1175 Toronto Canada 2005

[24] Y Yu Y Li and J Li ldquoParameter identification and sensitivityanalysis of an improved LuGre friction model for magnetorhe-ological elastomer base isolatorrdquo Meccanica vol 50 no 11 pp2691ndash2707 2015

[25] H Dou and Y Yang ldquoFurther understanding on fluid flowthrough multi-porous media in low-permeability reservoirsrdquoPetroleum Exploration and Development vol 39 no 5 pp 674ndash682 2012

[26] I Giorgio and D Scerrato ldquoMulti-scale concrete model withrate-dependent internal frictionrdquo European Journal of Environ-mental and Civil Engineering pp 1ndash19 2016

[27] X Wang H Ni and R Wang ldquob Modeling and analyzing themovement of drill string while being rocked on the groundrdquoJournal of Natural Gas Science Engineering pp 39-28 2017

[28] Z F Li ldquoFundamental equations and its applications fordynamical analysis of rod and pipe string in oil and gas wellsrdquoActa Petrolei Sinica vol 20 no 3 pp 87ndash90 1999

[29] T Piatkowski ldquoDahl and LuGre dynamic friction models -The analysis of selected propertiesrdquo Mechanism and MachineTheory vol 73 pp 91ndash100 2014

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VLSI Design

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Shock and Vibration

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