Research ArticleBelt Conveyor Dynamic Characteristics and Influential Factors

Junxia Li 12 and Xiaoxu Pang3

1College of Mechanical Engineering Taiyuan University of Technology Taiyuan 030024 China2Shanxi Provincial Engineering Laboratory (Research Center) for Mine Fluid Control Taiyuan 030024 China3Henan University of Science and Technology Luoyang 471027 China

Correspondence should be addressed to Junxia Li 1983767665qqcom

Received 13 October 2017 Accepted 30 January 2018 Published 30 April 2018

Academic Editor Francesco Pellicano

Copyright copy 2018 Junxia Li and Xiaoxu Pang This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper uses the Kelvin-Voigt viscoelastic model to establish the continuous dynamic equations for tail hammer tension beltconveyors The viscoelastic continuity equations are solved using the generalized coordinate method We analyze various factorsinfluencing longitudinal vibration of the belt conveyor by simulation and propose a control strategy to limit the vibration Theproposed approach and control strategywere verified by several experimental researches and casesTheproposed approach providesimproved accuracy for dynamic design of belt conveyors

1 Introduction

Belt conveyors are an integrated transmission and carryingmechanism with length sometimes extending several thou-sandmeters In traditional design and analysis of belt convey-ors vibration and impact are usually ignored and only staticdesign is considered However to ensure the safety of con-veyor operation for this restricted analysis designers mustincrease the safety factor which increases production costs

Many research groups have conducted dynamic analysisof large belt conveyors to reduce production cost and opti-mize conveyor performance [1 2]The conveyor belt was firstmodeled as an elastic body and then a viscoelastic body toincorporate viscoelastic characteristics of belt cover layer

In the early 1960s the former Soviet Union began to studyconveyor dynamics However due to the limited scienceand technology at that time the starting characteristicsfor constant acceleration or AC motors were studied byusing impulse principles and stress wave propagation in theconveyor belt on the basis of a simplifiedmechanicmodel [3]A series of later studies atHannoverUniversity of Technologyin Germany established the traveling wave theory Furtherstudies investigated conveyor dynamic characteristics [4 5]

Harrison Robert and James amongst others investigatedstarting and braking characteristics of steel wire rope core

conveyors and lateral bending vibration of the conveyor beltThey also analyzed stress wave propagation speed in theconveyor belt based on the theory of elastic and stress wavesand developed various relevant models [6ndash8]

Computer simulation of belt conveyor dynamiccharacteristics was presented by the Taiyuan Universityof Science and Technology using a Kelvin viscoelasticmodel and belt conveyor stability was analyzed in terms ofthe transverse vibration [9] Transverse vibration was alsostudied at Xirsquoan University of Science and Technology andShandong University of Science and Technology obtainingthe relationship between transverse vibration and speedand belt conveyor tension to provide a theoretical basis beltconveyor development [10 11]

Starting and braking curves horizontal turning andbroken band detection of belt conveyors were studied in theLiaoning Technical University using finite element analysis[12 13] A model of the whole belt conveyor was establishedusing the discrete dynamic method and dynamic simulationsoftware was constructed at Northeastern University Theconveyor dynamic characteristics under different boundaryconditions were studied experimentally and the conveyordynamic tension under different conditions was simulated[14 15]

HindawiShock and VibrationVolume 2018 Article ID 8106879 13 pageshttpsdoiorg10115520188106879

2 Shock and Vibration

Figure 1

Modern conveyor design methods were proposed on thebasis of analysis of the vibration characteristics by the Shang-hai Jiao Tong University and Shanghai Normal University[16ndash18]

However previous and current researches have mainlyfocused on discrete conveyor models Although viscoelas-ticity has been considered it has usually been simplified asan elastic model and the actual conveyor dynamic modelhas rarely been considered The current paper establishesthe dynamic equation for tail hammer tension belt conveyormodel based on theKelvin-Voigt viscoelasticmodel adoptingthe generalized coordinate method to solve the viscoelasticcontinuity equation Conveyor natural frequency and lon-gitudinal vibration characteristics are analyzed to provide amore accurate method for conveyor dynamic design

2 Dynamic Equation for Belt Conveyors

The Kelvin-Voigt model comprises a linear spring anddamper in parallel The model is applicable to simulatethe stress response of viscoelastic material However when119889120576119889119905 = 0 (120576 is total strain 119905 is time) the model can besimplified to the elastomer constitutive relationship as shownin Figure 1 Strains (1205761 1205762) on the two elements of the modelare the same and the stress (120590) is the sum of the spring (1205901)and damper stresses (1205902)

120590 = 1205901 + 1205902 = 1198641205761 + 1205791198891205762119889119905 (1)

where

120576 = 1205761 = 1205762 (2)

119864 is elastic modulus of conveyor belt and 120579 is viscositycoefficient

Solving (1) and (2)

120590 = 119864(1 + 120583 119889119889119905) 120576 (3)

which is the constitutive differential equation for the Kelvin-Voigt model reflecting creep behavior of viscoelastic materi-als

This paper considers the belt conveyor as a continuousbody and the conveyor dynamic behavior is described bypartial differential equations Figure 2 shows a typical tailhammer tensioning belt conveyorThe following assumptionsare made for establishing the conveyor mathematical model[19 20]

A Compared to longitudinal vibration of conveyor beltthe effect of transverse vibration is negligible

B Conveyor belt shearing and bending stress is negligi-ble

C Conveyor belt length change caused by vertical varia-tion is negligible

D Transverse deformation caused by conveyor belt lon-gitudinal tension is negligible

When starting a belt conveyor besides being subjected tostatic tension the conveyor belt is also subjected to dynamictension which is influenced by the conveyor speed changeSuppose that at time 119905 the displacement of some pointfrom the origin is 119880(119909 119905) The displacement includes staticdisplacement 119908(119909 119905) caused by the conveyor belt weightand hammer and dynamic displacement 119906(119909 119905) arising fromdynamic tension If the conveyor rigid body translationalacceleration is 119886(119905) then the conveyor absolute accelerationis 12059721199061205971199052 + 119886(119905)

From (3) the tension of the conveyor belt at some point119909 is

119878 (119909 119905) = 119864119861(120597119880120597119909 + 120583 1205972119880120597119905120597119909) (4)

where 119861 is the belt widthIgnoring conveyor running resistance the dynamic equa-

tion for conveyor longitudinal vibration can be expressed as

119902119889119909(12059721198801205971199052 + 119886 (119905)) = 120597119878120597119909119889119909 + 119902119892119889119909 (5)

where 119902 1199021 = 119902RO + 119902119861 + 119902119866 and 1199022 = 119902RU + 119902119861 are theconveyor belt equivalent mass per unit length in general andfor the carrying and return branches respectively 119902RU is themass per unit length of the rotary part of the supportingroller of the return branch 119902RO is the mass per unit lengthof the rotary part of the supporting roller of the carryingbranch 119902119861 is the mass per unit length of conveyor belt 119902119866is the material mass per unit length of conveyor belt 119892 isgravitational acceleration

Substituting (4) into (5) and introducing wave velocityparameter 119888

1198882 = 119864119861119902 (6)

Shock and Vibration 3

dxl

x

Figure 2

Considering belt conveyor dynamic characteristics thedifferential equation for viscoelastic longitudinal vibrationneglecting static displacement is [21]

12059721199061205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721199061205971199092 minus 119886 (119905) (7)

where 119886(119905) is the rigid body acceleration of conveyor beltWhen 120583 = 0 (7) can be simplified to the partial

differential equation of the elastic rod that is the one-dimensional wave equationThe boundary conditions for (7)are

119906 (0 119905) = 0120597119906 (119897 119905)120597119909 = 119872119892

2119864119861(8)

where 119872 is the weight of heavy hammer And the initialconditions are

119906 (119909 0) = 0120597119906 (119909 0)

120597119905 = 0 (9)

3 Kinetic Equation

31 Obtaining Homogeneous Boundary Conditions Equation(7) is a nonhomogeneous partial differential equation Toobtain a homogeneous equation the boundary conditionsmust be homogenized Suppose

119906 (119909 119905) = 119867 (119909 119905) + 119882 (119909 119905) (10)

Then an appropriate choice for119882(119909 119905) can make the bound-ary condition of119867(119909 119905) homogeneous

120597119882 (119871 119905)120597119909 = 119872119892

2119864119861119882(0 119905) = 0

(11)

and to meet the boundary condition requirements

119882(119909 119905) = 1198721198922119864119861 (119909 minus 119897) (12)

119906 (119909 119905) = 119867 (119909 119905) + 1198721198922119864119861 (119909 minus 119897) (13)

Substituting (13) into (9)

119867(119909 0) = 1198721198922119864119861 (119909 minus 119897) (14)

120597119867 (119909 119905)120597119905 = 0 (15)

and solving the partial derivative of 119909 and 119905 from (15)

12059721198671205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721198671205971199092 minus 119886 (119905) (16)

Thus the homogeneous boundary conditions are

120597119867 (0 119905)120597119909 = 0119867 (119897 119905) = 0119867 (119909 0) = 119872119892

2119864119861 (119909 minus 119897) 120597119867 (119909 0)

120597119905 = 0

(17)

32 Solution of Nonhomogeneous Equation Equation (16)is equivalent to the forced vibration of a single degree offreedom and its solution is divided into homogeneous andspecial solutions Suppose

119867(119909 119905) = ℎ (119909 119905) + 119908 (119909 119905) (18)

where ℎ(119909 119905) and 119908(119909 119905) are the special and homogeneoussolutions respectively Then (16) can be separated into ahomogeneous solution

12059721199081205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721199081205971199092

120597119908 (0 119905)120597119909 = 0119908 (119897 119905) = 0119908 (119909 0) = minus119872119892

2119864119861 (119909 minus 119897) 120597119908 (119909 0)

120597119905 = 0

(19)

4 Shock and Vibration

and special solution

1205972ℎ1205971199052 = 1198882 (1 + 120583 120597

120597119905)1205972ℎ1205971199092 minus 119886 (119905)

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(20)

ℎ (119909 0) = 0120597ℎ (119909 0)

120597119905 = 0 (21)

Using the method of separation of variables (18) is usedto determine the boundary conditions

Suppose 120578 = 120582119871 then120572 = 120578 tan 120578 (22)

where 120572 is the ratio of the equivalent mass per unit lengthof the carrying or return branch to half the mass of theheavy hammer that is 120572 = 2119902119897119872 Equation (22) isa transcendental equation with infinitely many solutionswhose shape function can be expressed as

119883119898 = sin 120582119898119909 = sin120578119898119897 119909 (23)

ℎ (119909 119905) = infinsum119898=1

119902119898 (119905) sin 120578119898119909119897 (24)

where (24) satisfies

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(25)

Let ℎ(119909 119905) = 0 and substitute (24) into (21) then differen-tiate multiply by sin(120578119898119897) on both sides and integrate

infinsum119898=1

[11990210158401015840119898 + 119888212058312058221199021015840119898 + 11988821205822119902119898]

sdot int1198970sin(120578119898119897 119909) sin(

120578119899119897 119909) 119889119909 = 119886 (119905)

sdot int1198970sin(120578119898119897 119909) 119889119909

(26)

By orthogonality if 119899 = 119898

int1198970sin1015840 (120578119899119909119897 ) sin1015840 (120578119898119909119897 ) = 0 (27)

and (26) can be simplified to

11990210158401015840119898 + 120583119888212058221199021015840119898 + 11988821205822119902119898 = 2120582119897119872119886 (119905) (28)

which has an infinite number ofmutually independentmodalequations and its form is similar to that of damped forced

vibration of single degree of freedom Therefore it can besolved by the method of single degree of freedom withgeneral solution

119902119898 = 119890minus120585120596119898119905120596119889 int119905

02120582119897119872119890120585120596119898120591119886 (119905) sin120596119889 (119905 minus 120591) 119889120591 (29)

where 119908119898 = 119888120578119898119897 is the conveyor natural vibrationfrequency 120585 = 1205831198881199081198982 is the conveyor damping coefficientand 119908119889 = 119908119898radic1 minus 1205852 is the conveyor damped naturalfrequency

The subscript 119898 for 119908119898 means that when 119898 is a naturalnumber it gets a corresponding natural frequency all ofwhich are the natural frequencies From (29) the conveyornatural frequency is not unique but has unlimited discretevalues and there is no natural frequency between any twodiscrete values When 119898 = 1 the natural frequency isthe fundamental frequency Vibration at the fundamentalfrequency tends to dominate the free and forced vibrationof the system When the conveyor starts the fundamentalfrequency is the earliest resonating frequency and the firstfrequency to avoid or break through when operating Thusidentifying the fundamental frequency is the top priority

The dynamic equation for conveyor longitudinal vibra-tion can be expressed as

119906 (119909 119905)= 1199021198972119864119861infinsum119898=1

sin 120582119898119909120578119898120596119889 int1199050119890minus120585120596119898(119905minus120591)119886 (120591) sin120596119889 (119905 minus 120591) 119889120591 (30)

Substituting (30) into (4) the analytical solution for thedynamic tension of the conveyorrsquos longitudinal vibration is

119904 (119909 119905) = 119902119897 infinsum119898=1

cos 120582119898119909120596119889 [119860 (119905) + 1205831198601015840 (119905)] (31)

where 119860(119905) = int1199050 119890minus120585119908(119905minus120591)119886(120591) sin119908119889(119905 minus 120591)119889120591From (30) and (31) maximum displacement occurs at

the pulley-tension position and maximum dynamic tensionoccurs at the trend point of the pulley-driving These factorsalso affect conveyor vibration characteristics such as carryingcapacity length tension acceleration and damping coeffi-cient

4 Impact of Various Factors on Vibration

41 Viscous Damping Effect

411 Acceleration Time Response Assuming that the beltconveyor adopts rectangular acceleration to start 119886(119905) = 119886119898This is equivalent to a stepped signal input and time responsecharacteristics can be obtained by substituting into (31)

119860 (119905) = 119886119898 [1 minus 119890minus120585120596119898119905radic1 minus 1205852 cos (120596119889119905 minus 120601)] (32)

where 120601 = tanminus1120585radic1 minus 1205852

Shock and Vibration 5

= 0 = 02 = 04

= 06 = 08

t (s)T

A(t)

0

am

2am

Figure 3

Table 1 Overshoot for different damping coefficients

Dampingcoefficient (120585) 0 02 04 06 08 1

Overshoot () 100 1147 486 059 001 0

Figure 3 shows the time response characteristics from(32) when 0 lt 120585 lt 1 and the following conclusions can bedrawn from Figure 3 and (32) and (29)

A The longitudinal vibration dynamical equation understep input is typical of second-order oscillation wherethe natural and damping frequencies are functions ofthe load ratio

B Underdamped vibration occurs as the damping coef-ficient changes from 0 to 1 As damping increasesmaximum overshoot and transient time decreasepeak time increases and stability improves

C From the performance index of second-order sys-tems maximum system overshoot is 119872119901 = (1radic1 minus 1205852)119890minus((120587+4)120585radic1minus1205852) Table 1 shows overshoot fordifferent damping coefficients

Table 1 shows that maximum overshoot decreases andsystem stability improves with increasing 120585 When 120585 ge 04overshoot is lt5 Thus the system has good stability when120585 ge 04412 Dynamic Tension Characteristics Using (32) and (31)we set 119902 = 2167 kgm 119897 = 845m 1205781 = 152 1199081 = 2333Hzand 120585 = 02 06 and 08 Figure 4 shows dynamic tensions atcarrying branches and the meeting point of the drive drumand belt conveyor under heavy load

Maximum dynamic tension in the conveyor belt occursat the drive drum and gradually reduces away from thedrumDynamic tension fluctuation amplitude decreases withincreasing 120585 which is consistent with the time response char-acteristics and indicates that viscous damping increases thebelt dissipation capacity As 120585 increases energy dissipationincreases and stability improves However dynamic tensionon the conveyor belt increases with increasing 120585 and smallerdynamic tension is better for belt conveyor designThereforesmaller damping is a desirable design criterion Combining

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

14

16

SN

times104

Damping coefficient 02Damping coefficient 06Damping coefficient 08

Figure 4

1 2 3 4 5 6 7 80t (s)

4

6

8

10

12

14

SN

times104

Loading ratio 5Loading ratio 75Loading ratio 10

Figure 5

time response characteristics 120585 = 04ndash06 produces lessdynamic tension and improved stability

42 Tension Effects Using the heavy hammer tension beltconveyor as an example the equivalent hammerweight varieswith the level of tension From 120572 = 2119902119897119872 the correspondingnatural frequencies are 2 213 and 219Hz while the loadratios between the carrying branches and hammer at full loadare 5 75 and 10 Figure 5 shows conveyor dynamic tensionunder different tensions when 120585 = 04

Conveyor belt tension decreases with increasing tensionThe maximum dynamic tension at the meeting point of thedrive drum was 1197 1130 and 1084 kN respectively Con-sequently to ensure normal operation increasing tension caneffectively reduce the conveyor belt dynamic tension

43 Transport Capacity Effects Transport capacity is themajor factor that determines the required belt conveyorpowerGenerally the designer determines the required powerbased on full load or the harshest conditions Under normal

6 Shock and Vibration

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

SN

times104

Full loadNo loadHalf volume

Figure 6

1 2 3 4 5 6 7 80t (s)

3456789

1011

SN

times104

Heavy hammerConstant forceForced winch

Figure 7

operating conditions the belt conveyor dynamic charac-teristics will usually be significantly different for differentloadings Figure 6 shows dynamic tension response for nohalf and full load conditions

Dynamic tension at the meeting point of the drive drumunder no half and full load conditions was 4795 7629 and9835 kN respectively Thus dynamic tension at the meetingpoint of the drive drum increases with increasing transportcapacity but the relationship is nonlinear Because the naturalvibration frequencies of the belt conveyor are different fordifferent loads dynamic tension under a given load cannotbe deduced directly from dynamic tension under a differentload

44 Tension Method Effects There are three major belttension methods heavy hammer constant force and fixedwinch Figure 7 shows the dynamic tension for thesemethodswhen startingwith constant accelerationMaximumdynamictension at the meeting point of the drive drum was 98351009 and 1075 kN respectively Considering the peak start-ing dynamic tension heavy hammer tension is superior tothe methods fixed winch tension produces the maximum

0

4

2

6

8

10

12

SN

times104

05 1 15 2 25 3 35 4 45 50t (s)

V = 2ＧＭ

V = 3ＧＭ

V = 4ＧＭ

Figure 8

Table 2 Simulation parameters for the considered belt conveyor

Parameter Symbol and valueCarrying capacity 119876 = 2000 thHaul distance 119871 = 500mBelt width 119861 = 12mStable operation speed V0 = 315msWeight of carrying idlers 1198661 = 660 kgMounting distance 1198971199051 = 3mWeight of return idlers 1198662 = 370 kgMounting distance 1198971199052 = 3mLinear mass per unit length 119902119861 = 624 kgmCross-sectional area 119860 = 0024 times 12 = 00288m2

Elasticity modulus 119864 = 65 times 5000 times 1030024 = 1354 times109 Pa

Rheological constant 120583 = 0015Initial tension 119865 = 450 kN

dynamic tension whereas constant automatic tension is verysimilar to the heavy hammermethodThis is consistent sincethe constant force tension method was developed to simulateand replace heavy hammer tension

45 Belt Velocity Effects Figure 8 shows dynamic tension fordifferent belt velocities V = 2 3 and 4ms with constantacceleration starting Maximum dynamic tension increaseswith increasing V and maximum dynamic tensions at themeeting point of drive drum were 4371 6557 and 1062 kNTherefore belt conveyor dynamic tension increases withincreasing belt velocity

5 Simulations

The dynamic acceleration and tension of the belt conveyorsystemwere simulated for large capacity high speed and longdistance transport Table 2 shows the basic parameters forthe chosen conveyor system comprising steel cord ST-5000

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

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004

a(Ｇ

2s

)

A(t)

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2s

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00005

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)0

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15 30 45 60 75 900t (s)

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2010 4030 500t (s)

0

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a(Ｇ

2s

)

A(t)

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a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

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(N)

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times105 times105 times104

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15 30 45 60 75 900t (s)

(a)

5000

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0

Sd (N

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times104

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Sd (N

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10 20 30 40 500t (s)

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Sd (N

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times104 times104 times104

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50 100 1500t (s)

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20 40 600t (s)

Sd (N

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times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

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Shock and Vibration 3

dxl

x

Figure 2

Considering belt conveyor dynamic characteristics thedifferential equation for viscoelastic longitudinal vibrationneglecting static displacement is [21]

12059721199061205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721199061205971199092 minus 119886 (119905) (7)

where 119886(119905) is the rigid body acceleration of conveyor beltWhen 120583 = 0 (7) can be simplified to the partial

differential equation of the elastic rod that is the one-dimensional wave equationThe boundary conditions for (7)are

119906 (0 119905) = 0120597119906 (119897 119905)120597119909 = 119872119892

2119864119861(8)

where 119872 is the weight of heavy hammer And the initialconditions are

119906 (119909 0) = 0120597119906 (119909 0)

120597119905 = 0 (9)

3 Kinetic Equation

31 Obtaining Homogeneous Boundary Conditions Equation(7) is a nonhomogeneous partial differential equation Toobtain a homogeneous equation the boundary conditionsmust be homogenized Suppose

119906 (119909 119905) = 119867 (119909 119905) + 119882 (119909 119905) (10)

Then an appropriate choice for119882(119909 119905) can make the bound-ary condition of119867(119909 119905) homogeneous

120597119882 (119871 119905)120597119909 = 119872119892

2119864119861119882(0 119905) = 0

(11)

and to meet the boundary condition requirements

119882(119909 119905) = 1198721198922119864119861 (119909 minus 119897) (12)

119906 (119909 119905) = 119867 (119909 119905) + 1198721198922119864119861 (119909 minus 119897) (13)

Substituting (13) into (9)

119867(119909 0) = 1198721198922119864119861 (119909 minus 119897) (14)

120597119867 (119909 119905)120597119905 = 0 (15)

and solving the partial derivative of 119909 and 119905 from (15)

12059721198671205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721198671205971199092 minus 119886 (119905) (16)

Thus the homogeneous boundary conditions are

120597119867 (0 119905)120597119909 = 0119867 (119897 119905) = 0119867 (119909 0) = 119872119892

2119864119861 (119909 minus 119897) 120597119867 (119909 0)

120597119905 = 0

(17)

32 Solution of Nonhomogeneous Equation Equation (16)is equivalent to the forced vibration of a single degree offreedom and its solution is divided into homogeneous andspecial solutions Suppose

119867(119909 119905) = ℎ (119909 119905) + 119908 (119909 119905) (18)

where ℎ(119909 119905) and 119908(119909 119905) are the special and homogeneoussolutions respectively Then (16) can be separated into ahomogeneous solution

12059721199081205971199052 = 1198882 (1 + 120583 120597

120597119905)12059721199081205971199092

120597119908 (0 119905)120597119909 = 0119908 (119897 119905) = 0119908 (119909 0) = minus119872119892

2119864119861 (119909 minus 119897) 120597119908 (119909 0)

120597119905 = 0

(19)

4 Shock and Vibration

and special solution

1205972ℎ1205971199052 = 1198882 (1 + 120583 120597

120597119905)1205972ℎ1205971199092 minus 119886 (119905)

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(20)

ℎ (119909 0) = 0120597ℎ (119909 0)

120597119905 = 0 (21)

Using the method of separation of variables (18) is usedto determine the boundary conditions

Suppose 120578 = 120582119871 then120572 = 120578 tan 120578 (22)

where 120572 is the ratio of the equivalent mass per unit lengthof the carrying or return branch to half the mass of theheavy hammer that is 120572 = 2119902119897119872 Equation (22) isa transcendental equation with infinitely many solutionswhose shape function can be expressed as

119883119898 = sin 120582119898119909 = sin120578119898119897 119909 (23)

ℎ (119909 119905) = infinsum119898=1

119902119898 (119905) sin 120578119898119909119897 (24)

where (24) satisfies

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(25)

Let ℎ(119909 119905) = 0 and substitute (24) into (21) then differen-tiate multiply by sin(120578119898119897) on both sides and integrate

infinsum119898=1

[11990210158401015840119898 + 119888212058312058221199021015840119898 + 11988821205822119902119898]

sdot int1198970sin(120578119898119897 119909) sin(

120578119899119897 119909) 119889119909 = 119886 (119905)

sdot int1198970sin(120578119898119897 119909) 119889119909

(26)

By orthogonality if 119899 = 119898

int1198970sin1015840 (120578119899119909119897 ) sin1015840 (120578119898119909119897 ) = 0 (27)

and (26) can be simplified to

11990210158401015840119898 + 120583119888212058221199021015840119898 + 11988821205822119902119898 = 2120582119897119872119886 (119905) (28)

which has an infinite number ofmutually independentmodalequations and its form is similar to that of damped forced

vibration of single degree of freedom Therefore it can besolved by the method of single degree of freedom withgeneral solution

119902119898 = 119890minus120585120596119898119905120596119889 int119905

02120582119897119872119890120585120596119898120591119886 (119905) sin120596119889 (119905 minus 120591) 119889120591 (29)

where 119908119898 = 119888120578119898119897 is the conveyor natural vibrationfrequency 120585 = 1205831198881199081198982 is the conveyor damping coefficientand 119908119889 = 119908119898radic1 minus 1205852 is the conveyor damped naturalfrequency

The subscript 119898 for 119908119898 means that when 119898 is a naturalnumber it gets a corresponding natural frequency all ofwhich are the natural frequencies From (29) the conveyornatural frequency is not unique but has unlimited discretevalues and there is no natural frequency between any twodiscrete values When 119898 = 1 the natural frequency isthe fundamental frequency Vibration at the fundamentalfrequency tends to dominate the free and forced vibrationof the system When the conveyor starts the fundamentalfrequency is the earliest resonating frequency and the firstfrequency to avoid or break through when operating Thusidentifying the fundamental frequency is the top priority

The dynamic equation for conveyor longitudinal vibra-tion can be expressed as

119906 (119909 119905)= 1199021198972119864119861infinsum119898=1

sin 120582119898119909120578119898120596119889 int1199050119890minus120585120596119898(119905minus120591)119886 (120591) sin120596119889 (119905 minus 120591) 119889120591 (30)

Substituting (30) into (4) the analytical solution for thedynamic tension of the conveyorrsquos longitudinal vibration is

119904 (119909 119905) = 119902119897 infinsum119898=1

cos 120582119898119909120596119889 [119860 (119905) + 1205831198601015840 (119905)] (31)

where 119860(119905) = int1199050 119890minus120585119908(119905minus120591)119886(120591) sin119908119889(119905 minus 120591)119889120591From (30) and (31) maximum displacement occurs at

the pulley-tension position and maximum dynamic tensionoccurs at the trend point of the pulley-driving These factorsalso affect conveyor vibration characteristics such as carryingcapacity length tension acceleration and damping coeffi-cient

4 Impact of Various Factors on Vibration

41 Viscous Damping Effect

411 Acceleration Time Response Assuming that the beltconveyor adopts rectangular acceleration to start 119886(119905) = 119886119898This is equivalent to a stepped signal input and time responsecharacteristics can be obtained by substituting into (31)

119860 (119905) = 119886119898 [1 minus 119890minus120585120596119898119905radic1 minus 1205852 cos (120596119889119905 minus 120601)] (32)

where 120601 = tanminus1120585radic1 minus 1205852

Shock and Vibration 5

= 0 = 02 = 04

= 06 = 08

t (s)T

A(t)

0

am

2am

Figure 3

Table 1 Overshoot for different damping coefficients

Dampingcoefficient (120585) 0 02 04 06 08 1

Overshoot () 100 1147 486 059 001 0

Figure 3 shows the time response characteristics from(32) when 0 lt 120585 lt 1 and the following conclusions can bedrawn from Figure 3 and (32) and (29)

A The longitudinal vibration dynamical equation understep input is typical of second-order oscillation wherethe natural and damping frequencies are functions ofthe load ratio

B Underdamped vibration occurs as the damping coef-ficient changes from 0 to 1 As damping increasesmaximum overshoot and transient time decreasepeak time increases and stability improves

C From the performance index of second-order sys-tems maximum system overshoot is 119872119901 = (1radic1 minus 1205852)119890minus((120587+4)120585radic1minus1205852) Table 1 shows overshoot fordifferent damping coefficients

Table 1 shows that maximum overshoot decreases andsystem stability improves with increasing 120585 When 120585 ge 04overshoot is lt5 Thus the system has good stability when120585 ge 04412 Dynamic Tension Characteristics Using (32) and (31)we set 119902 = 2167 kgm 119897 = 845m 1205781 = 152 1199081 = 2333Hzand 120585 = 02 06 and 08 Figure 4 shows dynamic tensions atcarrying branches and the meeting point of the drive drumand belt conveyor under heavy load

Maximum dynamic tension in the conveyor belt occursat the drive drum and gradually reduces away from thedrumDynamic tension fluctuation amplitude decreases withincreasing 120585 which is consistent with the time response char-acteristics and indicates that viscous damping increases thebelt dissipation capacity As 120585 increases energy dissipationincreases and stability improves However dynamic tensionon the conveyor belt increases with increasing 120585 and smallerdynamic tension is better for belt conveyor designThereforesmaller damping is a desirable design criterion Combining

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

14

16

SN

times104

Damping coefficient 02Damping coefficient 06Damping coefficient 08

Figure 4

1 2 3 4 5 6 7 80t (s)

4

6

8

10

12

14

SN

times104

Loading ratio 5Loading ratio 75Loading ratio 10

Figure 5

time response characteristics 120585 = 04ndash06 produces lessdynamic tension and improved stability

42 Tension Effects Using the heavy hammer tension beltconveyor as an example the equivalent hammerweight varieswith the level of tension From 120572 = 2119902119897119872 the correspondingnatural frequencies are 2 213 and 219Hz while the loadratios between the carrying branches and hammer at full loadare 5 75 and 10 Figure 5 shows conveyor dynamic tensionunder different tensions when 120585 = 04

Conveyor belt tension decreases with increasing tensionThe maximum dynamic tension at the meeting point of thedrive drum was 1197 1130 and 1084 kN respectively Con-sequently to ensure normal operation increasing tension caneffectively reduce the conveyor belt dynamic tension

43 Transport Capacity Effects Transport capacity is themajor factor that determines the required belt conveyorpowerGenerally the designer determines the required powerbased on full load or the harshest conditions Under normal

6 Shock and Vibration

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

SN

times104

Full loadNo loadHalf volume

Figure 6

1 2 3 4 5 6 7 80t (s)

3456789

1011

SN

times104

Heavy hammerConstant forceForced winch

Figure 7

operating conditions the belt conveyor dynamic charac-teristics will usually be significantly different for differentloadings Figure 6 shows dynamic tension response for nohalf and full load conditions

Dynamic tension at the meeting point of the drive drumunder no half and full load conditions was 4795 7629 and9835 kN respectively Thus dynamic tension at the meetingpoint of the drive drum increases with increasing transportcapacity but the relationship is nonlinear Because the naturalvibration frequencies of the belt conveyor are different fordifferent loads dynamic tension under a given load cannotbe deduced directly from dynamic tension under a differentload

44 Tension Method Effects There are three major belttension methods heavy hammer constant force and fixedwinch Figure 7 shows the dynamic tension for thesemethodswhen startingwith constant accelerationMaximumdynamictension at the meeting point of the drive drum was 98351009 and 1075 kN respectively Considering the peak start-ing dynamic tension heavy hammer tension is superior tothe methods fixed winch tension produces the maximum

0

4

2

6

8

10

12

SN

times104

05 1 15 2 25 3 35 4 45 50t (s)

V = 2ＧＭ

V = 3ＧＭ

V = 4ＧＭ

Figure 8

Table 2 Simulation parameters for the considered belt conveyor

Parameter Symbol and valueCarrying capacity 119876 = 2000 thHaul distance 119871 = 500mBelt width 119861 = 12mStable operation speed V0 = 315msWeight of carrying idlers 1198661 = 660 kgMounting distance 1198971199051 = 3mWeight of return idlers 1198662 = 370 kgMounting distance 1198971199052 = 3mLinear mass per unit length 119902119861 = 624 kgmCross-sectional area 119860 = 0024 times 12 = 00288m2

Elasticity modulus 119864 = 65 times 5000 times 1030024 = 1354 times109 Pa

Rheological constant 120583 = 0015Initial tension 119865 = 450 kN

dynamic tension whereas constant automatic tension is verysimilar to the heavy hammermethodThis is consistent sincethe constant force tension method was developed to simulateand replace heavy hammer tension

45 Belt Velocity Effects Figure 8 shows dynamic tension fordifferent belt velocities V = 2 3 and 4ms with constantacceleration starting Maximum dynamic tension increaseswith increasing V and maximum dynamic tensions at themeeting point of drive drum were 4371 6557 and 1062 kNTherefore belt conveyor dynamic tension increases withincreasing belt velocity

5 Simulations

The dynamic acceleration and tension of the belt conveyorsystemwere simulated for large capacity high speed and longdistance transport Table 2 shows the basic parameters forthe chosen conveyor system comprising steel cord ST-5000

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

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4 Shock and Vibration

and special solution

1205972ℎ1205971199052 = 1198882 (1 + 120583 120597

120597119905)1205972ℎ1205971199092 minus 119886 (119905)

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(20)

ℎ (119909 0) = 0120597ℎ (119909 0)

120597119905 = 0 (21)

Using the method of separation of variables (18) is usedto determine the boundary conditions

Suppose 120578 = 120582119871 then120572 = 120578 tan 120578 (22)

where 120572 is the ratio of the equivalent mass per unit lengthof the carrying or return branch to half the mass of theheavy hammer that is 120572 = 2119902119897119872 Equation (22) isa transcendental equation with infinitely many solutionswhose shape function can be expressed as

119883119898 = sin 120582119898119909 = sin120578119898119897 119909 (23)

ℎ (119909 119905) = infinsum119898=1

119902119898 (119905) sin 120578119898119909119897 (24)

where (24) satisfies

120597ℎ (0 119905)120597119909 = 0ℎ (119897 119905) = 0

(25)

Let ℎ(119909 119905) = 0 and substitute (24) into (21) then differen-tiate multiply by sin(120578119898119897) on both sides and integrate

infinsum119898=1

[11990210158401015840119898 + 119888212058312058221199021015840119898 + 11988821205822119902119898]

sdot int1198970sin(120578119898119897 119909) sin(

120578119899119897 119909) 119889119909 = 119886 (119905)

sdot int1198970sin(120578119898119897 119909) 119889119909

(26)

By orthogonality if 119899 = 119898

int1198970sin1015840 (120578119899119909119897 ) sin1015840 (120578119898119909119897 ) = 0 (27)

and (26) can be simplified to

11990210158401015840119898 + 120583119888212058221199021015840119898 + 11988821205822119902119898 = 2120582119897119872119886 (119905) (28)

which has an infinite number ofmutually independentmodalequations and its form is similar to that of damped forced

vibration of single degree of freedom Therefore it can besolved by the method of single degree of freedom withgeneral solution

119902119898 = 119890minus120585120596119898119905120596119889 int119905

02120582119897119872119890120585120596119898120591119886 (119905) sin120596119889 (119905 minus 120591) 119889120591 (29)

where 119908119898 = 119888120578119898119897 is the conveyor natural vibrationfrequency 120585 = 1205831198881199081198982 is the conveyor damping coefficientand 119908119889 = 119908119898radic1 minus 1205852 is the conveyor damped naturalfrequency

The subscript 119898 for 119908119898 means that when 119898 is a naturalnumber it gets a corresponding natural frequency all ofwhich are the natural frequencies From (29) the conveyornatural frequency is not unique but has unlimited discretevalues and there is no natural frequency between any twodiscrete values When 119898 = 1 the natural frequency isthe fundamental frequency Vibration at the fundamentalfrequency tends to dominate the free and forced vibrationof the system When the conveyor starts the fundamentalfrequency is the earliest resonating frequency and the firstfrequency to avoid or break through when operating Thusidentifying the fundamental frequency is the top priority

The dynamic equation for conveyor longitudinal vibra-tion can be expressed as

119906 (119909 119905)= 1199021198972119864119861infinsum119898=1

sin 120582119898119909120578119898120596119889 int1199050119890minus120585120596119898(119905minus120591)119886 (120591) sin120596119889 (119905 minus 120591) 119889120591 (30)

Substituting (30) into (4) the analytical solution for thedynamic tension of the conveyorrsquos longitudinal vibration is

119904 (119909 119905) = 119902119897 infinsum119898=1

cos 120582119898119909120596119889 [119860 (119905) + 1205831198601015840 (119905)] (31)

where 119860(119905) = int1199050 119890minus120585119908(119905minus120591)119886(120591) sin119908119889(119905 minus 120591)119889120591From (30) and (31) maximum displacement occurs at

the pulley-tension position and maximum dynamic tensionoccurs at the trend point of the pulley-driving These factorsalso affect conveyor vibration characteristics such as carryingcapacity length tension acceleration and damping coeffi-cient

4 Impact of Various Factors on Vibration

41 Viscous Damping Effect

411 Acceleration Time Response Assuming that the beltconveyor adopts rectangular acceleration to start 119886(119905) = 119886119898This is equivalent to a stepped signal input and time responsecharacteristics can be obtained by substituting into (31)

119860 (119905) = 119886119898 [1 minus 119890minus120585120596119898119905radic1 minus 1205852 cos (120596119889119905 minus 120601)] (32)

where 120601 = tanminus1120585radic1 minus 1205852

Shock and Vibration 5

= 0 = 02 = 04

= 06 = 08

t (s)T

A(t)

0

am

2am

Figure 3

Table 1 Overshoot for different damping coefficients

Dampingcoefficient (120585) 0 02 04 06 08 1

Overshoot () 100 1147 486 059 001 0

Figure 3 shows the time response characteristics from(32) when 0 lt 120585 lt 1 and the following conclusions can bedrawn from Figure 3 and (32) and (29)

A The longitudinal vibration dynamical equation understep input is typical of second-order oscillation wherethe natural and damping frequencies are functions ofthe load ratio

B Underdamped vibration occurs as the damping coef-ficient changes from 0 to 1 As damping increasesmaximum overshoot and transient time decreasepeak time increases and stability improves

C From the performance index of second-order sys-tems maximum system overshoot is 119872119901 = (1radic1 minus 1205852)119890minus((120587+4)120585radic1minus1205852) Table 1 shows overshoot fordifferent damping coefficients

Table 1 shows that maximum overshoot decreases andsystem stability improves with increasing 120585 When 120585 ge 04overshoot is lt5 Thus the system has good stability when120585 ge 04412 Dynamic Tension Characteristics Using (32) and (31)we set 119902 = 2167 kgm 119897 = 845m 1205781 = 152 1199081 = 2333Hzand 120585 = 02 06 and 08 Figure 4 shows dynamic tensions atcarrying branches and the meeting point of the drive drumand belt conveyor under heavy load

Maximum dynamic tension in the conveyor belt occursat the drive drum and gradually reduces away from thedrumDynamic tension fluctuation amplitude decreases withincreasing 120585 which is consistent with the time response char-acteristics and indicates that viscous damping increases thebelt dissipation capacity As 120585 increases energy dissipationincreases and stability improves However dynamic tensionon the conveyor belt increases with increasing 120585 and smallerdynamic tension is better for belt conveyor designThereforesmaller damping is a desirable design criterion Combining

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

14

16

SN

times104

Damping coefficient 02Damping coefficient 06Damping coefficient 08

Figure 4

1 2 3 4 5 6 7 80t (s)

4

6

8

10

12

14

SN

times104

Loading ratio 5Loading ratio 75Loading ratio 10

Figure 5

time response characteristics 120585 = 04ndash06 produces lessdynamic tension and improved stability

42 Tension Effects Using the heavy hammer tension beltconveyor as an example the equivalent hammerweight varieswith the level of tension From 120572 = 2119902119897119872 the correspondingnatural frequencies are 2 213 and 219Hz while the loadratios between the carrying branches and hammer at full loadare 5 75 and 10 Figure 5 shows conveyor dynamic tensionunder different tensions when 120585 = 04

Conveyor belt tension decreases with increasing tensionThe maximum dynamic tension at the meeting point of thedrive drum was 1197 1130 and 1084 kN respectively Con-sequently to ensure normal operation increasing tension caneffectively reduce the conveyor belt dynamic tension

43 Transport Capacity Effects Transport capacity is themajor factor that determines the required belt conveyorpowerGenerally the designer determines the required powerbased on full load or the harshest conditions Under normal

6 Shock and Vibration

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

SN

times104

Full loadNo loadHalf volume

Figure 6

1 2 3 4 5 6 7 80t (s)

3456789

1011

SN

times104

Heavy hammerConstant forceForced winch

Figure 7

operating conditions the belt conveyor dynamic charac-teristics will usually be significantly different for differentloadings Figure 6 shows dynamic tension response for nohalf and full load conditions

Dynamic tension at the meeting point of the drive drumunder no half and full load conditions was 4795 7629 and9835 kN respectively Thus dynamic tension at the meetingpoint of the drive drum increases with increasing transportcapacity but the relationship is nonlinear Because the naturalvibration frequencies of the belt conveyor are different fordifferent loads dynamic tension under a given load cannotbe deduced directly from dynamic tension under a differentload

44 Tension Method Effects There are three major belttension methods heavy hammer constant force and fixedwinch Figure 7 shows the dynamic tension for thesemethodswhen startingwith constant accelerationMaximumdynamictension at the meeting point of the drive drum was 98351009 and 1075 kN respectively Considering the peak start-ing dynamic tension heavy hammer tension is superior tothe methods fixed winch tension produces the maximum

0

4

2

6

8

10

12

SN

times104

05 1 15 2 25 3 35 4 45 50t (s)

V = 2ＧＭ

V = 3ＧＭ

V = 4ＧＭ

Figure 8

Table 2 Simulation parameters for the considered belt conveyor

Parameter Symbol and valueCarrying capacity 119876 = 2000 thHaul distance 119871 = 500mBelt width 119861 = 12mStable operation speed V0 = 315msWeight of carrying idlers 1198661 = 660 kgMounting distance 1198971199051 = 3mWeight of return idlers 1198662 = 370 kgMounting distance 1198971199052 = 3mLinear mass per unit length 119902119861 = 624 kgmCross-sectional area 119860 = 0024 times 12 = 00288m2

Elasticity modulus 119864 = 65 times 5000 times 1030024 = 1354 times109 Pa

Rheological constant 120583 = 0015Initial tension 119865 = 450 kN

dynamic tension whereas constant automatic tension is verysimilar to the heavy hammermethodThis is consistent sincethe constant force tension method was developed to simulateand replace heavy hammer tension

45 Belt Velocity Effects Figure 8 shows dynamic tension fordifferent belt velocities V = 2 3 and 4ms with constantacceleration starting Maximum dynamic tension increaseswith increasing V and maximum dynamic tensions at themeeting point of drive drum were 4371 6557 and 1062 kNTherefore belt conveyor dynamic tension increases withincreasing belt velocity

5 Simulations

The dynamic acceleration and tension of the belt conveyorsystemwere simulated for large capacity high speed and longdistance transport Table 2 shows the basic parameters forthe chosen conveyor system comprising steel cord ST-5000

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

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Shock and Vibration 5

= 0 = 02 = 04

= 06 = 08

t (s)T

A(t)

0

am

2am

Figure 3

Table 1 Overshoot for different damping coefficients

Dampingcoefficient (120585) 0 02 04 06 08 1

Overshoot () 100 1147 486 059 001 0

Figure 3 shows the time response characteristics from(32) when 0 lt 120585 lt 1 and the following conclusions can bedrawn from Figure 3 and (32) and (29)

A The longitudinal vibration dynamical equation understep input is typical of second-order oscillation wherethe natural and damping frequencies are functions ofthe load ratio

B Underdamped vibration occurs as the damping coef-ficient changes from 0 to 1 As damping increasesmaximum overshoot and transient time decreasepeak time increases and stability improves

C From the performance index of second-order sys-tems maximum system overshoot is 119872119901 = (1radic1 minus 1205852)119890minus((120587+4)120585radic1minus1205852) Table 1 shows overshoot fordifferent damping coefficients

Table 1 shows that maximum overshoot decreases andsystem stability improves with increasing 120585 When 120585 ge 04overshoot is lt5 Thus the system has good stability when120585 ge 04412 Dynamic Tension Characteristics Using (32) and (31)we set 119902 = 2167 kgm 119897 = 845m 1205781 = 152 1199081 = 2333Hzand 120585 = 02 06 and 08 Figure 4 shows dynamic tensions atcarrying branches and the meeting point of the drive drumand belt conveyor under heavy load

Maximum dynamic tension in the conveyor belt occursat the drive drum and gradually reduces away from thedrumDynamic tension fluctuation amplitude decreases withincreasing 120585 which is consistent with the time response char-acteristics and indicates that viscous damping increases thebelt dissipation capacity As 120585 increases energy dissipationincreases and stability improves However dynamic tensionon the conveyor belt increases with increasing 120585 and smallerdynamic tension is better for belt conveyor designThereforesmaller damping is a desirable design criterion Combining

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

14

16

SN

times104

Damping coefficient 02Damping coefficient 06Damping coefficient 08

Figure 4

1 2 3 4 5 6 7 80t (s)

4

6

8

10

12

14

SN

times104

Loading ratio 5Loading ratio 75Loading ratio 10

Figure 5

time response characteristics 120585 = 04ndash06 produces lessdynamic tension and improved stability

42 Tension Effects Using the heavy hammer tension beltconveyor as an example the equivalent hammerweight varieswith the level of tension From 120572 = 2119902119897119872 the correspondingnatural frequencies are 2 213 and 219Hz while the loadratios between the carrying branches and hammer at full loadare 5 75 and 10 Figure 5 shows conveyor dynamic tensionunder different tensions when 120585 = 04

Conveyor belt tension decreases with increasing tensionThe maximum dynamic tension at the meeting point of thedrive drum was 1197 1130 and 1084 kN respectively Con-sequently to ensure normal operation increasing tension caneffectively reduce the conveyor belt dynamic tension

43 Transport Capacity Effects Transport capacity is themajor factor that determines the required belt conveyorpowerGenerally the designer determines the required powerbased on full load or the harshest conditions Under normal

6 Shock and Vibration

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

SN

times104

Full loadNo loadHalf volume

Figure 6

1 2 3 4 5 6 7 80t (s)

3456789

1011

SN

times104

Heavy hammerConstant forceForced winch

Figure 7

operating conditions the belt conveyor dynamic charac-teristics will usually be significantly different for differentloadings Figure 6 shows dynamic tension response for nohalf and full load conditions

Dynamic tension at the meeting point of the drive drumunder no half and full load conditions was 4795 7629 and9835 kN respectively Thus dynamic tension at the meetingpoint of the drive drum increases with increasing transportcapacity but the relationship is nonlinear Because the naturalvibration frequencies of the belt conveyor are different fordifferent loads dynamic tension under a given load cannotbe deduced directly from dynamic tension under a differentload

44 Tension Method Effects There are three major belttension methods heavy hammer constant force and fixedwinch Figure 7 shows the dynamic tension for thesemethodswhen startingwith constant accelerationMaximumdynamictension at the meeting point of the drive drum was 98351009 and 1075 kN respectively Considering the peak start-ing dynamic tension heavy hammer tension is superior tothe methods fixed winch tension produces the maximum

0

4

2

6

8

10

12

SN

times104

05 1 15 2 25 3 35 4 45 50t (s)

V = 2ＧＭ

V = 3ＧＭ

V = 4ＧＭ

Figure 8

Table 2 Simulation parameters for the considered belt conveyor

Parameter Symbol and valueCarrying capacity 119876 = 2000 thHaul distance 119871 = 500mBelt width 119861 = 12mStable operation speed V0 = 315msWeight of carrying idlers 1198661 = 660 kgMounting distance 1198971199051 = 3mWeight of return idlers 1198662 = 370 kgMounting distance 1198971199052 = 3mLinear mass per unit length 119902119861 = 624 kgmCross-sectional area 119860 = 0024 times 12 = 00288m2

Elasticity modulus 119864 = 65 times 5000 times 1030024 = 1354 times109 Pa

Rheological constant 120583 = 0015Initial tension 119865 = 450 kN

dynamic tension whereas constant automatic tension is verysimilar to the heavy hammermethodThis is consistent sincethe constant force tension method was developed to simulateand replace heavy hammer tension

45 Belt Velocity Effects Figure 8 shows dynamic tension fordifferent belt velocities V = 2 3 and 4ms with constantacceleration starting Maximum dynamic tension increaseswith increasing V and maximum dynamic tensions at themeeting point of drive drum were 4371 6557 and 1062 kNTherefore belt conveyor dynamic tension increases withincreasing belt velocity

5 Simulations

The dynamic acceleration and tension of the belt conveyorsystemwere simulated for large capacity high speed and longdistance transport Table 2 shows the basic parameters forthe chosen conveyor system comprising steel cord ST-5000

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

6 Shock and Vibration

1 2 3 4 5 6 7 80t (s)

2

4

6

8

10

12

SN

times104

Full loadNo loadHalf volume

Figure 6

1 2 3 4 5 6 7 80t (s)

3456789

1011

SN

times104

Heavy hammerConstant forceForced winch

Figure 7

operating conditions the belt conveyor dynamic charac-teristics will usually be significantly different for differentloadings Figure 6 shows dynamic tension response for nohalf and full load conditions

Dynamic tension at the meeting point of the drive drumunder no half and full load conditions was 4795 7629 and9835 kN respectively Thus dynamic tension at the meetingpoint of the drive drum increases with increasing transportcapacity but the relationship is nonlinear Because the naturalvibration frequencies of the belt conveyor are different fordifferent loads dynamic tension under a given load cannotbe deduced directly from dynamic tension under a differentload

44 Tension Method Effects There are three major belttension methods heavy hammer constant force and fixedwinch Figure 7 shows the dynamic tension for thesemethodswhen startingwith constant accelerationMaximumdynamictension at the meeting point of the drive drum was 98351009 and 1075 kN respectively Considering the peak start-ing dynamic tension heavy hammer tension is superior tothe methods fixed winch tension produces the maximum

0

4

2

6

8

10

12

SN

times104

05 1 15 2 25 3 35 4 45 50t (s)

V = 2ＧＭ

V = 3ＧＭ

V = 4ＧＭ

Figure 8

Table 2 Simulation parameters for the considered belt conveyor

Parameter Symbol and valueCarrying capacity 119876 = 2000 thHaul distance 119871 = 500mBelt width 119861 = 12mStable operation speed V0 = 315msWeight of carrying idlers 1198661 = 660 kgMounting distance 1198971199051 = 3mWeight of return idlers 1198662 = 370 kgMounting distance 1198971199052 = 3mLinear mass per unit length 119902119861 = 624 kgmCross-sectional area 119860 = 0024 times 12 = 00288m2

Elasticity modulus 119864 = 65 times 5000 times 1030024 = 1354 times109 Pa

Rheological constant 120583 = 0015Initial tension 119865 = 450 kN

dynamic tension whereas constant automatic tension is verysimilar to the heavy hammermethodThis is consistent sincethe constant force tension method was developed to simulateand replace heavy hammer tension

45 Belt Velocity Effects Figure 8 shows dynamic tension fordifferent belt velocities V = 2 3 and 4ms with constantacceleration starting Maximum dynamic tension increaseswith increasing V and maximum dynamic tensions at themeeting point of drive drum were 4371 6557 and 1062 kNTherefore belt conveyor dynamic tension increases withincreasing belt velocity

5 Simulations

The dynamic acceleration and tension of the belt conveyorsystemwere simulated for large capacity high speed and longdistance transport Table 2 shows the basic parameters forthe chosen conveyor system comprising steel cord ST-5000

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Shock and Vibration 7

conveyor belt head drive hydraulic tail and constant forceautomatic tension

51 Simulation for Three Starting Regimes Let 120573 = 1198791198791where 1198791 = 21205871199081 is the fundamental vibration period ofthe conveyor belt From (32) if 1205961 = 07 rads then 1198791 = 89 sFigures 9 and 10 show dynamic acceleration for three startingregimes with 120573 = 3 5 10 15 20 and 25 and different startingtime 119879 for the system (119909 = 05119871)

The different starting regimes become more similarand acceleration maximum acceleration reduces as timeincreases Dynamic tension fluctuation also converges andreduces with increasing time

The parabolic starting regime and increased starting timeto 15ndash20 times fundamental vibration period effectively reducedfluctuation andmaximum dynamic acceleration and tensioneffectively limiting longitudinal vibration shock across thewhole system

52 Dynamic Simulation of the Parabolic Starting RegimeAs shown in Figures 11 and 12 the simulation responsesof the belt conveyor to dynamic acceleration and tensionversus time and displacement were obtained with parabolicacceleration

When starting time T = 80 s although conveyor beltacceleration fluctuations are significant at different displace-ments maximum acceleration (Figure 11) and dynamic ten-sion (Figure 12) are relatively stable However maximumdynamic tension changes significantly with displacementAcceleration fluctuation at 119909 = 0 is very small whereasit is very large at 119909 = 119871 Maximum dynamic accelerationis relatively stable while changes and maximum dynamictension at 119909 = 0 and 119909 = 119871 show opposite trend to dynamicacceleration

Acceleration of the carrying segment for thewhole systemis increasing moving from the head drive drum to tailtensioning but the dynamic tension of the bearing segmentdecreases during the process of closing the tail Thereforein addition to choosing the starting regime and control-ling starting time further strategies were required to limitdynamic tension and acceleration volatility and maximumThe auxiliary equipment can be used in the middle part ofthe system such as driving the middle linear friction wheelarranging rational position and spacing and number of idlersand choosing appropriate drums to further enhance controlof longitudinal vibration shocks for the overall system

6 Experiments

The belt conveyor simulation run at 2ms starts for 10ndash15times fundamental period Using a parabolic starting regimedynamic experimental data of tension and acceleration werecollected for the physical conveyor system described inTable 3

61 Acceleration Measurement Figure 13 shows the hallsensor used to measure the belt running speed The feedbackpulse signal was collected by using a data acquisition system

Table 3 Experimental belt conveyor system parameters

Parameter ValueHaul distance 30mBelt width 500mmMaximum speed under steadyoperation 25ms

Angle 2∘

Drive drum diameter 500mmTurnabout electric drum diameter 500m

Carrying rollers 35∘ grooving rollers 12mspacing

Return rollers Pinto idlers 24m spacingMotor Y-160M 4-5 kW 380VRetarder K87171-AE5Multiloop disc brake Constant hydraulic automatictensioning

Variable frequency soft starter

to obtain dynamic speed measurements If 1198981 feedbackpulses are received from the hall sensor in 119879119888 seconds 119901 isthe number of pulses for each roller rotations and 119863 is theroller diameter then the speed of rotation is

119899 = 601198981119901119879119888 (33)

and the belt dynamic acceleration is

119886 = 212058711989811199011198791198882 119863 (34)

62 Tension Measurement Figure 14 shows the tensiontesting device composed of a tension sensor and rollersDynamic tension can be derived from the detected pressuredevice geometry If 120579 is the surrounding angle of the belt androller in the device 119865119873 is the measured pressure and 119866 isthe gravity force of the rollers then the belt tension can beexpressed as

119878 = 12 (119865119873 minus 119866) csc 120579 (35)

63 Simulation Site To collect suitable data during theexperiment the dynamic testing device was installed closeto the drive drum of the tail Yet testing points of dynamictension are close to the head and drum of the tail the devicesin the dynamic simulation experiment of acceleration andtension are shown in Figures 15 and 16

64 Experimental Results Figures 17 and 18 show the mea-sured belt acceleration and tension at the tail starting for10 times fundamental period and Figure 19 shows the dynamictension at the head

The tension cylinder oil inlet of the hydraulic automaticconstant tension device starts to supply oil to the former at 5 s

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

8 Shock and Vibration

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02

a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)0

0005001

0015002

0025003

a(Ｇ

2s

)

0

002

004

006

008

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

20 400t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(a)

00005

0010015

0020025

0030035

004

a(Ｇ

2s

)

A(t)

a(t)

0

01

02025

015

005a(Ｇ

2s

)

00005

0010015

0020025

003

a(Ｇ

2s

)

00005

0010015

0020025

003a

(Ｇ2s

)

0

005

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

25 50 75 100 125 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

00025

0050075

010125

015

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(b)

0005

01015

02025

03

0025005

007501

0125015

0175

002004006008

01

001002003004

001

002

003

004

0

001

002

003

004

0

005

a(Ｇ

2s

)

A(t)

a(t)

a(Ｇ

2s

)

0

a(Ｇ

2s

)

a(Ｇ

2s

)

0

012

a(Ｇ

2s

)

15 30 45 60 75 900t (s)

40 80 120 160 200 2400t (s)

30 60 90 120 150 1800t (s)

30 60 90 120 1500t (s)

5 10 15 20 25 300t (s)

2010 4030 500t (s)

0

02

a(Ｇ

2s

)

A(t)

a(t)

A(t)

a(t)

(c)

Figure 9

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Shock and Vibration 9

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

2

4

Sd (N

)

times104 times104 times104

5 10 15 20 25 300t (s)

0

1

2Sd

(N)

0

2

4

Sd (N

)

0

1

2

Sd (N

)

10 20 30 40 500t (s)

0

5

Sd (N

)

0

1

2

Sd (N

)

times105 times105 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

(a)

5000

10000

15000

0 30 60 90 120 150 180t (s)

25 50 75 100 125 1500t (s)

0

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

5

10

Sd (N

)

0

5

Sd (N

)

10 20 30 40 500t (s)

0

4

2

Sd (N

)

0

5000

10000

Sd (N

)

times104 times104 times104

40 80 120 160 200 2400t (s)

15 30 45 60 75 900t (s)

0

1

2

Sd (N

)

(b)

0 100 200t (s)

50 100 1500t (s)

0

5

Sd (N

)

times104

5 10 15 20 25 300t (s)

0

1

3

2

Sd (N

)

0

2

Sd (N

)

20 40 600t (s)

Sd (N

)

times105 times105 times105

100 200 3000t (s)

50 1000t (s)

minus5

0

5

Sd (N

)

times104

minus5

minus2

0

5

Sd (N

)

times104

minus5

0

1

minus1

(c)

Figure 10

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10 Shock and Vibration

5000

0 0

50

100

x (m)t (s)

minus005

0

005

01

A(m

Ｍ2)

Figure 11

5000

0 0

50

100

times104

x (m)t (s)

minus5

0

5

10

Sd (N

)

Figure 12

3 2 4 5

1

Figure 13

which makes belt tension approximately linearly increase tooperationally required initial tension (6 kN) In the following5ndash31 s the belt starts to move and the system starts reachingthe normal running speed (2ms) When the system is

running smoothly tension is small with the automatictension cylinder providing a relatively stable 43 kN Belttension at the tail is relatively stable due to dynamic bufferingof the hydraulic automatic constant tension device

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Shock and Vibration 11

321 4FN

S

Figure 14

Figure 15 The site map of acceleration test

Figure 16 The site map of tension test

Figures 20 and 21 show themeasured belt acceleration andtension at the tail starting for 15 times fundamental period andFigure 22 shows the dynamic tension at the head

When belt conveyor starts for 10 times fundamental periodpeak belt acceleration at the tail and tension at the head are0018ms2 and 629 kN respectively When the belt conveyorstarts for 15 times fundamental period peak belt acceleration atthe tail and tension at the head are 0075ms2 and 6079 kNrespectively Thus tension and acceleration are smaller when

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

001

002

003

004

005

006

007

008

009

010

011

012

A(m

Ｍ2)

Figure 17

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SN

Figure 18

starting for 10 times fundamental period than 15 and starting ismore stable

7 Conclusions

We can conclude the following

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Shock and Vibration

2 4 6 80 12 14 16 18 20 22 24 2610

t (s)

6000

6025

6050

6075

6100

6125

6150

6175

6200

6225

6250

6275

6300

SN

Figure 19

t (s)

0001002003004005006007008

A(m

Ｍ2)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

Figure 20

t (s)

0

40

38

36

34

32

50

48

46

44

42

30

28

26

24

22

20

18

16

14

12

108642

0500

1000150020002500300035004000450050005500600065007000

SN

Figure 21

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 400

t (s)

6020

6010

6030

6040

6050

6060

6070

6080

6000

SN

Figure 22

A A general solution was presented to simplify the vis-coelastic rod system into partial differential continu-ous longitudinal vibration equations for longitudinalvibration Also a general theoretical approach wasprovided to analyze similar systems

B Based on the longitudinal vibration dynamic equa-tions belt conveyor time response characteristicswere analyzed under different starting control strate-gies It was shown that the difference betweenmaximum acceleration and maximum accelerationresponse was less than 5 when starting time wasmore than 15 times fundamental vibration period and itcan effectively reduce longitudinal vibration

C Simulation results were experimentally verifiedD The effects on belt conveyor vibration characteristics

from damping tension carrying capacity tensionmode and belt speed were investigated and providea theoretical basis for design and manufacture of beltconveyors

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the New Century ExcellentTalents (Grant no NECT-12-1038) NSFC-Shanxi Coal BasedLow Carbon Joint Fund Focused on Supporting Project(Grant no U1510205) and Science and Technology Project ofShanxi Province (Grant no 2015031006-2)The authors grate-fully acknowledge the helpful discussions with the researchgroup and colleagues of Taiyuan University of technology

References

[1] L-P Zhu and W-L Jiang ldquoStudy on typical belt conveyor incoal mine of Chinardquo Journal of the China Coal Society vol 35no 11 pp 1916ndash1920 2010

[2] B H Wang J P Liu and S Lu ldquoAnalyzed development of thehigh-power and high-speed belt conveyorrdquo Mining Machineryvol 42 no 1 pp 27ndash30 2014

[3] A P Wiid and M Bagus ldquoPower belt technologyrdquo Bulk SolidsHandling vol 21 no 6 pp 602ndash607 2001

[4] L Frederick ldquoUpdating the Los Pelambres overland conveyorsystemrdquoMining Engineering vol 51 no 4 pp 35-36 1999

[5] G B Li Study on dynamic characteristics of the belt conveyor[PhD thesis] Shanghai Jiaotong University Shanghai China2003

[6] B Zuo W G Song and L L Wan ldquoComparative of thebelt conveyors starting ldquos curvesrdquo based on the traveling wavetheoryrdquoMining Machinery vol 39 no 10 pp 46ndash52 2011

[7] H W Zhao ldquoExperimental research on the rubber beltsdynamic characteristics of the large belt conveyorrdquo Science andTechnology Information vol 21 pp 549-550 2011

[8] Z L Ding Design and development of high-power and punchybelt conveyor [PhD thesis] Xirsquoan University of TechnologyXirsquoan China 2007

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Shock and Vibration 13

[9] X Li Dynamics simulation and software development of the beltconveyor system [PhD thesis] Taiyuan University of Scienceand Technology Taiyuan China 2014

[10] W G Song Design of the Universal Belt Conveyor ChinaMachine Press Beijing China 2006

[11] L K Nordell ldquoZISCO installs worlds longest troughed belt156km horizontally curved overland conveyorrdquo in Proceedingsof the BELTCON 9 Conference Republic of South Africa 1997

[12] D E Beckley ldquoDevelopment of low friction belt conveyors foroverland applicationsrdquo Bulk Solids Handling vol 11 no 4 pp795ndash799 1991

[13] L K Nordell ldquoChannar 20 km overland A flagship of modernbelt conveyor technologyrdquo Bulk Solids Handling vol 11 no 4pp 781-78 1991

[14] Y H Li ldquoAutomatic modeling and program development ofthe belt conveyorrsquos dynamic analysisrdquo Tech Rep LiaoningTechnical University Fuxin China 2002

[15] D I G Jones and M L Parin ldquoTechnique for measuringdamping properties of thin viscoelastic layersrdquo Journal of Soundand Vibration vol 24 no 2 pp 201ndash210 1972

[16] S NGaneriwala andCA Rotz ldquoFourier transformmechanicalanalysis for determining the nonlinear viscoelastic properties ofpolymersrdquoPolymer Engineeringamp Science vol 27 no 2 pp 165ndash178 1987

[17] L H Chen W Zhang and Y Q Liu ldquoModeling of nonlin-ear oscillations for viscoelastic moving belt using generalizedHamiltonrsquos principlerdquo Journal of Vibration and Acoustics vol129 no 1 pp 128ndash132 2007

[18] H Ding and L-Q Chen ldquoApproximate and numerical analysisof nonlinear forced vibration of axially moving viscoelasticbeamsrdquo Acta Mechanica Sinica vol 27 no 3 pp 426ndash437 2011

[19] G B Li Dynamics and Design of the Belt Conveyor ChinaMachine Press Beijing China 1998

[20] B Karolewski ldquoAn investigation of various conveyor belt drivesystems using amathematical modelrdquo Bulk Solids Handling vol6 no 2 pp 349ndash354 1986

[21] Y J LiDynamic Study and Engineering Design of theMulti-RopeFriction Hoist System Coal Industry Publishing House BeijingChina 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom