analysisandexperimentalstudyonpressurecharacteristicsof ... · 2019. 4. 12. ·...

Research ArticleAnalysis and Experimental Study on Pressure Characteristics ofSupporting Roller Group of Pipe Belt Conveyor

Shuang Wang12 Deyong Li 2 and Kun Hu 12

1State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal MinesAnhui University of Science and Technology Huainan Anhui 232001 China2College of Mechanical Engineering Anhui University of Technology Huainan Anhui 232001 China

Correspondence should be addressed to Deyong Li lidyausteducn

Received 12 April 2019 Revised 19 July 2019 Accepted 22 July 2019 Published 1 August 2019

Academic Editor Roberto Nascimbene

Copyright copy 2019 ShuangWang et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at the problem in measuring the nonuniformly distributed pressure generated by the pipe belt conveyor when conveyingraw coals a hexagonal adjustable pressure measuring device for the idler group is proposed e dynamic model of the pipe beltconveyor clamping-type roller group is established In order to simplify the calculation process of mechanical analysis the modalanalysis is carried out to determine the factors which will influence the pressure e pipe diameter and filling rate are selected asthe key control factors by the sensitive analysis of pressure of the pipe belt conveyor clamping type roller group An adjustablediameter-type supporting roller group experiment device is self-designed and the dynamic pressure change of the roller groupand each roller pressure are testede results show that the average error between the simulated and tested values of the pressureof the idler group at different filling rates is 73 the theoretical and simulated values of the pressure of the idler group are in goodagreement with the experimental values e study provides a theoretical basis and experimental reference for the design andapplication of pipe belt conveyors

1 Introduction

Nowadays countries around the world are shifting towards adevelopment model highlighted by green ecology and lowcarbon [1] However the environmental pollution which iscaused by a large amount of dust and scattering granulesgenerated by the bulk material transfer system during workhas raised more andmore attention in the conveyor industryaround the world [2] Many countries have proposed the useof environmentally friendly pipe belt conveyors to reducethe environmental pollution from the conveying process[3 4] Moreover a pipe belt conveyor has shown greatdevelopment prospects [5] because it overcomes theshortcomings of the traditional belt conveyor such as thesusceptibility of generating dust and scattering granules thevulnerability to which it is hampered by spatial restrictionsand the small turning inclination angle [6]

e conveyor belt of the pipe belt conveyor is guided bythe idler [7] Also the flat belt passing through the rollergradually takes the shape of a pipe belt to increase the

enveloping surface of the conveyor belt to the material andensure the enclosed conveying of the material [8] Zamiralovaet al studied the rotational resistance of the idlers of the pipebelt conveyer and reduced the resistance of the idler duringthe conveying process [9 10] e comparative analysis be-tween the force distribution of the pipe belt conveyer underno load and that of the traditional belt conveyor was con-ducted and the dynamic wear analysis of the rubber conveyorbelt of the pipe belt conveyer was performed by Fedorko et al[11 12] Molnar et al presents design and verification ofregressionmodels for prediction of pipe conveyor belt contactforces on idler rolls Several criteria have been used to verifythe presented regression models [13 14] Lodewijks tested therolling resistance coefficient between the rubber conveyor beltand the idlers and investigated the turning characteristicsinvolving large inclination angle of the round belt conveyor[15 16] Professor Weigang Song pointed out the unrea-sonableness of the original shaping theory of the transitionsegment proposed the circular section theory of the transitionsegment of the pipe belt conveyor and provided the shaping

HindawiShock and VibrationVolume 2019 Article ID 7061847 7 pageshttpsdoiorg10115520197061847

diagram of the transition segment of the pipe belt conveyorusing computer simulation [17 18] Based on the differentialelements shaping theory Professor Houhua Yang analyzedthemechanical behaviors of the adhesive tape in the transitionsegment of the pipe using a computer simulation technologyand the geometric distribution of mechanical behaviors wasobtained through simulating the mechanical behaviors of thetarget under the influence of complex forces [19]

However many of the above studies were just focused onthe no-load conveying of the pipe belt conveyor but theconveying of raw coal and other materials was not taken intoaccount In this paper a pressure testing device for thehexagonal adjustable idlers was proposed to solve the difficultyinmeasuring the nonuniformly distributed pressure generatedby the pipe belt conveyor when conveying raw coals More-over a mechanical model of the bottom-type idlers of the pipebelt conveyor was establisheden the sensitivity analysis onthe factors influencing the pressure of the idlers was completedto reduce the workload of themechanical analysis of the idlerse main control factors were then found based on theweighting to be the pipe diameter and the filling rate Finallythe conclusions of the theoretical analysis were verifiedthrough a series of simulations and tests

2 Pressure Analysis of Idlers of PipeBelt Conveyor

e 167 km pipe belt conveyor developed by the project teamin 2019 has been successfully applied as shown in Figure 1

21 Analysis of Total Pressure of Idlers As shown in Figure 2θ is the deflection angle of materials α is the angle related tothematerial filling rate and β is the repose angle of materials

e conveyor beltrsquos total pressure Fi (i 1 2 6)applied on the idler is

Fl1 Fl6 12ρgR

2L 1113946

(π3)

0[cos θ + sin α +(cos α minus sin θ)tan β]

times nmax + nmin( 1113857cos2 θ + 2 sin2 θx1113960 1113961dθ

(1)

Fl2 Fl5ρgR2L

21113946

(2π3)

(π3)[cos θ + sin α +(cos α minus sin θ)tan β]

times nmax + nmin( 1113857cos2 θ + 2 sin2 θ1113960 1113961dθ

(2)

Fl3 Fl4 ρgR2L

21113946π

(2π3)[cos θ + sin α +(cos α minus sin θ)tan β]


(3)

Fc1 Fc2 Fc3 Fc4 Fc5 Fc6 π3

L times

3

radicEbb3

18 1 minus μxμy1113872 1113873R2

(4)

Fg1 Fg6 qB

BtimesπRL

3cos

π3

Fg2 Fg5 qB

BtimesπRL

3cos

2π3

Fg3 Fg4 qB

BtimesπRL

3cos π

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

Fi Fli + Fci + Fgi (6)

It can be concluded from the aforementioned equationsthat idlers of the pipe belt conveyor are subject to threeforces including belt lateral pressure Fli(i 1 2 6) beltcircling force Fci(i 1 2 6) and belt gravity forceFgi(i 1 2 6) [20]

As can be seen in equations (1)ndash(6) variables related tothe force of idlers are density of material transportation ρmaterial filling height h distance between idlers L piperadius R elastic modulus of the conveyor belt Eb width ofthe conveyor belt B etc e sensitivity analysis is needed toselect a design variable having the greatest effect on thepressure of idlers from optimizable variables ie when the

Figure 1 e pipe conveyor

F1

F2

F3F4

F5

F6

ABC

θdθ

αβ

h

1

2

3

4

5

6

Figure 2 Clip-type bottom roller material element diagram

2 Shock and Vibration

variable changes slightly the changes of the pressure of theidler groups are regarded as sensitivity [21 22]

3 Determination of Pressure OptimizationVariables of Idlers of Pipe Belt Conveyor

31 SensitivityAnalysisModel In engineering design designsensitivity is often defined as the derivative of structuralresponse obtained by design calculation with respect to adesign variable at is a structural response representsstructural response function F(X)rsquos sensitivity to designvariable xi at a specified design point xi

Sxi(X)

zF(X)

zxi

(7)

where Sxireflects structural response function F(X)rsquos

monotonicity to design variable xi e absolute value of Sxi

reflects structural response function F(X)rsquos sensitivity todesign variable xi the greater this value is the more sensitiveto xi the function F(X) is e precondition of equation (7) isthat the modification of xi must be very small However inpractical application difficulties in changing different designvariables by same values vary while difficulties in changingoptimization variables by same percentages are basically thesame For example when the material density is large andthe pipe diameter is small changing the material density by01 is easier than changing the pipe diameter by 01erefore this paper proposes the concept of pressureweight of idlers and takes this weight as the basis for op-timizing parameters

32 Weight Concept For any multivariate differentiablefunction the following equation can be derived usingTaylorrsquos expansion

F x1 x2 xn( 1113857 zF

zx1

zF

zx2

zF

zxn

1113888 1113889 x1 x2 xn( 1113857T

+ H

(8)

where H is a higher-order terme partial derivative term in equation (8) is function

variablersquos sensitivity to function When the higher-orderterm is ignored the multivariate function can be approxi-mated as

F x1 x2 xn( 1113857 asympzF

zx1x1 +

zF

zx2x2 + middot middot middot +

zF

zxn

xn (9)

After the weight vector λ (λ1 λ2 λn)T is defined tomake it become the percentage of function value corre-sponding to any one variable to total function value theweight can be expressed as

λi zF

zxi

xi

F x1 x2 xn( 1113857 i 1 2 n (10)

In optimization design the pressure of idlers is usuallythe implicit function of various optimization design

variables and can be expanded according to equation (10)where the partial derivative term is the sensitivity of pressureof idlers and the weight vector represents the ldquocontributionrdquoratio of all variables to pressure of idlers e larger theweight of the optimization variable is the greater effect onidlers the variable has

As can be seen in Figure 3 when the sensitivity is used asthe basis of selection the material density and belt widthhave a high sensitivity and the remaining parameters aresmall when the weight is used as the basis of selection thepipe diameter and material filling height have a great effecton the pressure of idlers Obviously the latter matches theactual situation better Positive weights indicate that thepressure of idlers increases with the increase of the pa-rameter and negative weights indicate that the pressure ofidlers increases with the decrease of the parameter

e analysis results show that the variable that has a greateffect on the pressure of idlers is pipe diameter and materialfilling height erefore final optimization variables aredetermined to be pipe diameter and material filling height(filling rate)

4 Simulation and Experimental Verification

41 Discrete Element Simulation Analysis e difficulty ofseparation of raw coal and mixed gangue after mining is in-creased due to the nonuniform particle size erefore it isnecessary to crush a large amount of raw coal and ganguebefore transportation by the pipe belt conveyor In general ajaw crusher can be used to crush large coal gangue to 18ndash48mm [20] erefore the simulation coal radius is 20mmand the conveyor beltmodel adopts themoving-planemodel tosimulate the uniform linear movement of the conveyor belt Inthis paper the recovery coefficient and static friction coefficientbetween coal and conveyor belt are set up with reference todocument [22] the simulation process as shown in Figure 4

Tables 1 and 2 are the pressure values of differentmeasuring areas with filling rates of 60 and 75

42 Test Design is test was set up on a self-designedhexagon pressure testing device with adjustable pipe di-ameter which consists of 6 linear feed guides 6 pressuresensors 1 external eight-way signal transformer and 1 eight-way paperless recorder as shown in Figure 5 e relevantparameters are as follows the adjustable range of pipe di-ameter is 150mmsim250mm the feeding of linear feed guidesis 150mm and the support bracket is made of aluminumalloy with density of 266times103 kgm3 and thickness of 4mm

During the test signals of 6 pressure sensors were de-tected within 150mmsim250mm of pipe diameter at no load60 or 75 filling rate and full load en the pressuresensorrsquos signals under different pipe diameters were ob-tained with the paperless recorder and computer and therelevant data were processed with signal processing software[21] e test principle and plan are shown in Figure 6

43 Test Results andDiscussion Six pressure sensorsrsquo signalsat no load 60 or 75 filling rate and full load were

Shock and Vibration 3

researched and analyzed by processing the test data withMATLAB numerical analysis software as shown in Figure 7

Figures 7(a)ndash7(d) give the test results obtained at noload 60 filling rate 75 filling rate and full load by

simulating the arrangement of hexagon idlers on 6 pressuresensors As can be seen from Figures 7(a)ndash7(d) No 1 and 6are subject to the largest pressure and unequal forces No 2and 5 are subject to a large pressure and unequal forces No3 and 4 are subject to the smallest pressure and unequalforces the whole force increases with the increase of pipediameter although each idler has different force trends It canbe known from the comparison of Figures 7(a)ndash7(d) thatwhen the filling rate and pipe diameter gradually increaseidlersrsquo force simulated by pressure sensors increases as awhole but the force distribution of each idler in idlers varieswhich are consistent with the actual situation

ρ h L R Eb b qB Bndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0Se

nsiti

vity

of t

he p

ress

ure o

f the

rolle

r gro

up

(a)


ndash10

0

10

20

30

40

50

Wei

ght o

f the

pre

ssur

e of t

he ro

ller g

roup

()

(b)

Figure 3 Simulation diagram (a) Sensitivity of the structural parameters on the pressure of the roller group (b) Weight of the structuralparameters on the pressure of the roller group

Measuringarea no 1

Measuringarea no 2

Measuringarea no 3

Measuringarea no 4

Measuringarea no 5

Measuringarea no 6

Figure 4 Simulation process

Table 1 Pressure value of the roller group at 60 filling rate

150mm 180mm 210mm 240mmMeasuring area no 1 49N 58N 73N 107NMeasuring area no 2 30N 40N 69N 79NMeasuring area no 3 17N 19N 18N 20NMeasuring area no 4 9N 12N 13N 15NMeasuring area no 5 7N 11N 19N 30NMeasuring area no 6 38N 65N 74N 131N



1

2

3

45

Figure 5 Test device 1 pressure transducer 2 linear feed guide3 conveyor belt 4 bracket 5 signal transmission line


e pipe diameter is set at 150mm Table 3 is thecomparison data table between the simulation value and thetest value when the filling rate is 60 and 75 respectively

From Table 3 we can see that the simulation value of theidler group is close to the test value and the average error isonly 73 From Figure 8 it can be concluded that the

4

5

6

3

2

1

1020

3040

50

150mm180mm

210mm240mm

(a)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(b)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(c)

4

5

6

3

2

1

4080

120160

200

150mm180mm

210mm240mm

(d)

Figure 7 Pressure diagram of the roller group under different pipe diameters (a) no load (b) 60 filling rate (c) 75 filling rate and (d) fullload

1 2

3

4 5

6

Figure 6 Schematic diagram of experimental test 1 pressure transducer 2 conveyor belt 3 linear feed guide 4 signal processor5 paperless recorder 6 PC


theoretical and simulated values of the pressure of the idlergroup are in good agreement with the experimental valuesand the values are close to each other e main sources oferrors in test results theory and simulation analysis areneglecting the length of the overlapping area after theconveyor belt of the pipe belt conveyor becomes circular andthe bending rigidity of the conveyor belt

5 Conclusions

In this paper a pressure testing device for the hexagonaladjustable idlers was proposed to solve the difficulty inmeasuring the nonuniformly distributed pressure generatedby the pipe belt conveyor when conveying raw coalsMoreover a mechanical model of the bottom-type idlers ofthe pipe belt conveyor was established en the sensitivityanalysis on the factors influencing the pressure of the idlers

was completed to reduce the workload of the mechanicalanalysis of the idlers e main control factors were thenfound based on the weighting to be the pipe diameter and thefilling rate Finally the conclusions of the theoretical analysiswere verified through a series of simulations and tests especific conclusions are as follows

(1) e mechanical model of the pinch-bottom idlergroup of the circular pipe belt conveyor is establishedby using the microelement method In order toreduce the workload of mechanical analysis of theidler group the sensitivity analysis of mechanicalmodel of the idler group is carried out and the pipediameter and filling rate are obtained as the maincontrolling factors of the pressure of the idler group

(2) Self-designed test is used to simulate the stress of thehexagonal roller group and the force distribution ofthe hexagonal roller group and the dynamic forcediagram of the hexagonal roller group under dif-ferent filling rates are obtained Comparing the forcesimulation value with the test value of the hexagonalroller set shows that the average error between themis only 73 e research provides theoretical ref-erence and experimental basis for the design of rawcoal conveying of the circular pipe belt conveyor

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestsregarding the publication of this paper

Authorsrsquo Contributions

Shuang WANG conceptualized the study Shuang WANGand Deyong LI formally analyzed the results ShuangWANG and KunHU obtained the funding Deyong LI wrotethe original draft

Acknowledgments

is research work was supported by the National NaturalScience Fund Project of China (grant no 51874004) NatureScience Research Project of Anhui Province (grant no1908085QE227) and Graduate innovation fund of AnhuiUniversity of Science and Technology (grant nos QN2018101 and QN 2018116)

References

[1] J-B Sheu and Y J Chen ldquoTransportation and economies ofscale in recycling low-value materialsrdquo Transportation Re-search Part B Methodological vol 65 pp 65ndash76 2014

[2] M R Phate and V H Tatwawadi ldquoMathematical models ofmaterial removal rate amp power consumption for dry turningof ferrous material using dimensional analysis in Indian

Table 3 Comparison of simulation and test results

Pressuresimulation (N) Pressure test (N) Error ()

1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89

Averageerror mdash mdash 73

1 2 3 4 5 60

10

20

30

40

50

60

70

Theoretical valueSimulation valueTest value

Pres

sure

(N)

Idler number

Figure 8 Pressure comparison of theoretical simulation and testrollers


prospectiverdquo Jordan Journal of Mechanical and IndustrialEngineering vol 9 no 1 pp 27ndash38 2015

[3] A Ullmann and A Dayan ldquoExhaust volume model for dustemission control of belt conveyor transfer pointsrdquo PowderTechnology vol 96 no 2 pp 139ndash147 1998

[4] F Zeng Q Wu X Chu and Z Yue ldquoMeasurement of bulkmaterial flow based on laser scanning technology for theenergy efficiency improvement of belt conveyorsrdquo Mea-surement vol 75 pp 230ndash243 2015

[5] M H A Elnaggar ldquoe optimization of thickness and per-meability of wick structure with different working fluids ofL-shape heat pipe for electronic coolingrdquo Jordan Journal ofMechanical and Industrial Engineering vol 8 no 3pp 119ndash125 2014

[6] M Barburski ldquoAnalysis of the pipe conveyor belt pressure onthe rollers on its circuitrdquo Journal of Industrial Textiles vol 45no 6 pp 1ndash16 2015

[7] M Andrejiova A Grincova D Marasova G Fedorko andV Molnar ldquoUsing logistic regression in tracing the signifi-cance of rubberndashtextile conveyor belt damagerdquoWear vol 318no 1-2 pp 145ndash152 2014

[8] M M Montazer-Rahmati and B Amini-Horri ldquoFrom lab-oratory experiments to design of a conveyor-belt dryer viamathematical modelingrdquo Drying Technology vol 23 no 12pp 2389ndash2420 2005

[9] M E Zamiralova and G Lodewijks ldquoMeasurement of a pipebelt conveyor contact forces and cross section deformation bymeans of the six-point pipe belt stiffness testing devicerdquoMeasurement vol 70 pp 232ndash246 2015

[10] M E Zamiralova and G Lodewijks ldquoPipe conveyor test rigsdesign application and test resultsmdashpart Crdquo Bulk SolidsHandling vol 35 no 1 pp 42ndash49 2015

[11] G Fedorko V Molnar J Zivcak M Dovica andN Husakova ldquoFailure analysis of textile rubber conveyor beltdamaged by dynamic wearrdquo Engineering Failure Analysisvol 28 pp 103ndash114 2013

[12] G Fedorko V Molnar M Dovica T Toth and M KopasldquoAnalysis of pipe conveyor belt damaged by thermal wearrdquoEngineering Failure Analysis vol 45 no 1 pp 41ndash48 2014

[13] V Molnar G Fedorko B Stehlıkova P Michalik andM Weiszer ldquoA regression model for prediction of pipeconveyor belt contact forces on idler rollsrdquo Measurementvol 46 no 10 pp 3910ndash3917 2013

[14] V Molnar G Fedorko B Stehlıkova Lrsquo Kudelas andN Husakova ldquoStatistical approach for evaluation of pipeconveyorrsquos belt contact forces on guide idlersrdquo Measurementvol 46 no 9 pp 3127ndash3135 2013

[15] G Lodewijks ldquoDetermination of rolling resistance of beltconveyors using rubber data fact or fictionrdquo Bulk SolidsHandling vol 23 no 6 pp 384ndash391 2003

[16] G Lodewijks K F Drenth and P S van der Mel ldquoerotation of pipe conveyorsrdquo in Proceedings of the Powder ampBulk Solids India pp 1ndash13 Mumbai India 2010

[17] W-G Song G-W Zhang and Y-S Deng ldquoComputersimulation and design of transition section of circular beltconveyorrdquo Journal of Northeast University (Natural ScienceEdition) vol 24 no 7 pp 692ndash695 2003

[18] W-G Song H-L Cheng Y-S Deng et al ldquoShaping design oftransition on pipe belt conveyorrdquo Hoisting and ConveyingMachinery vol 8 pp 7ndash10 2000

[19] H-H Yang and T Han ldquoAnalysis of mechanical charac-teristics of belt in transition section of circular tube beltconveyorrdquo Mining Machinery vol 3 pp 66-67 2006

[20] Y-C Guo SWang K Hu and D-Y Li ldquoOptimizing the pipediameter of the pipe belt conveyor based on discrete elementmethodrdquo 3D Research vol 7 no 1 pp 1ndash9 2016

[21] Y-C Guo S Wang K Hu and D-Y Li ldquoOptimization andexperimental study of transport section lateral pressure ofpipe belt conveyorrdquo Advanced Powder Technology vol 27no 4 pp 1318ndash1324 2016

[22] J Justice C Bower M Meitl M B Mooney M A Gubbinsand B Corbett ldquoWafer-scale integration of group IIIndashV laserson silicon using transfer printing of epitaxial layersrdquo NaturePhotonics vol 6 no 9 pp 610ndash614 2012


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VLSI Design



Shock and Vibration


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Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

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Journal ofEngineeringVolume 2018

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RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

diagram of the transition segment of the pipe belt conveyorusing computer simulation [17 18] Based on the differentialelements shaping theory Professor Houhua Yang analyzedthemechanical behaviors of the adhesive tape in the transitionsegment of the pipe using a computer simulation technologyand the geometric distribution of mechanical behaviors wasobtained through simulating the mechanical behaviors of thetarget under the influence of complex forces [19]

However many of the above studies were just focused onthe no-load conveying of the pipe belt conveyor but theconveying of raw coal and other materials was not taken intoaccount In this paper a pressure testing device for thehexagonal adjustable idlers was proposed to solve the difficultyinmeasuring the nonuniformly distributed pressure generatedby the pipe belt conveyor when conveying raw coals More-over a mechanical model of the bottom-type idlers of the pipebelt conveyor was establisheden the sensitivity analysis onthe factors influencing the pressure of the idlers was completedto reduce the workload of themechanical analysis of the idlerse main control factors were then found based on theweighting to be the pipe diameter and the filling rate Finallythe conclusions of the theoretical analysis were verifiedthrough a series of simulations and tests

2 Pressure Analysis of Idlers of PipeBelt Conveyor

e 167 km pipe belt conveyor developed by the project teamin 2019 has been successfully applied as shown in Figure 1

21 Analysis of Total Pressure of Idlers As shown in Figure 2θ is the deflection angle of materials α is the angle related tothematerial filling rate and β is the repose angle of materials

e conveyor beltrsquos total pressure Fi (i 1 2 6)applied on the idler is

Fl1 Fl6 12ρgR

2L 1113946

(π3)

0[cos θ + sin α +(cos α minus sin θ)tan β]

times nmax + nmin( 1113857cos2 θ + 2 sin2 θx1113960 1113961dθ

(1)

Fl2 Fl5ρgR2L

21113946

(2π3)

(π3)[cos θ + sin α +(cos α minus sin θ)tan β]


(2)

Fl3 Fl4 ρgR2L

21113946π

(2π3)[cos θ + sin α +(cos α minus sin θ)tan β]


(3)

Fc1 Fc2 Fc3 Fc4 Fc5 Fc6 π3

L times

3

radicEbb3

18 1 minus μxμy1113872 1113873R2

(4)

Fg1 Fg6 qB

BtimesπRL

3cos

π3

Fg2 Fg5 qB

BtimesπRL

3cos

2π3

Fg3 Fg4 qB

BtimesπRL

3cos π

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

Fi Fli + Fci + Fgi (6)

It can be concluded from the aforementioned equationsthat idlers of the pipe belt conveyor are subject to threeforces including belt lateral pressure Fli(i 1 2 6) beltcircling force Fci(i 1 2 6) and belt gravity forceFgi(i 1 2 6) [20]

As can be seen in equations (1)ndash(6) variables related tothe force of idlers are density of material transportation ρmaterial filling height h distance between idlers L piperadius R elastic modulus of the conveyor belt Eb width ofthe conveyor belt B etc e sensitivity analysis is needed toselect a design variable having the greatest effect on thepressure of idlers from optimizable variables ie when the

Figure 1 e pipe conveyor

F1

F2

F3F4

F5

F6

ABC

θdθ

αβ

h

1

2

3

4

5

6

Figure 2 Clip-type bottom roller material element diagram





Sxi(X)

zF(X)

zxi

(7)





F x1 x2 xn( 1113857 zF

zx1

zF

zx2

zF

zxn

1113888 1113889 x1 x2 xn( 1113857T

+ H

(8)




zx1x1 +

zF


zF

zxn

xn (9)


λi zF

zxi

xi

F x1 x2 xn( 1113857 i 1 2 n (10)
















ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0Se

nsiti

vity

of t

he p

ress

ure o

f the

rolle

r gro

up

(a)


ndash10

0

10

20

30

40

50

Wei

ght o

f the

pre

ssur

e of t

he ro

ller g

roup

()

(b)


Measuringarea no 1

Measuringarea no 2

Measuringarea no 3

Measuringarea no 4

Measuringarea no 5

Measuringarea no 6






1

2

3

45





4

5

6

3

2

1

1020

3040

50

150mm180mm

210mm240mm

(a)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(b)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(c)

4

5

6

3

2

1

4080

120160

200

150mm180mm

210mm240mm

(d)


1 2

3

4 5

6




5 Conclusions





Data Availability






Acknowledgments


References





1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89


1 2 3 4 5 60

10

20

30

40

50

60

70


Pres

sure

(N)

Idler number



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Sxi(X)

zF(X)

zxi

(7)





F x1 x2 xn( 1113857 zF

zx1

zF

zx2

zF

zxn

1113888 1113889 x1 x2 xn( 1113857T

+ H

(8)




zx1x1 +

zF


zF

zxn

xn (9)


λi zF

zxi

xi

F x1 x2 xn( 1113857 i 1 2 n (10)
















ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0Se

nsiti

vity

of t

he p

ress

ure o

f the

rolle

r gro

up

(a)


ndash10

0

10

20

30

40

50

Wei

ght o

f the

pre

ssur

e of t

he ro

ller g

roup

()

(b)


Measuringarea no 1

Measuringarea no 2

Measuringarea no 3

Measuringarea no 4

Measuringarea no 5

Measuringarea no 6






1

2

3

45





4

5

6

3

2

1

1020

3040

50

150mm180mm

210mm240mm

(a)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(b)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(c)

4

5

6

3

2

1

4080

120160

200

150mm180mm

210mm240mm

(d)


1 2

3

4 5

6




5 Conclusions





Data Availability






Acknowledgments


References





1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89


1 2 3 4 5 60

10

20

30

40

50

60

70


Pres

sure

(N)

Idler number



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0Se

nsiti

vity

of t

he p

ress

ure o

f the

rolle

r gro

up

(a)


ndash10

0

10

20

30

40

50

Wei

ght o

f the

pre

ssur

e of t

he ro

ller g

roup

()

(b)


Measuringarea no 1

Measuringarea no 2

Measuringarea no 3

Measuringarea no 4

Measuringarea no 5

Measuringarea no 6






1

2

3

45





4

5

6

3

2

1

1020

3040

50

150mm180mm

210mm240mm

(a)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(b)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(c)

4

5

6

3

2

1

4080

120160

200

150mm180mm

210mm240mm

(d)


1 2

3

4 5

6




5 Conclusions





Data Availability






Acknowledgments


References





1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89


1 2 3 4 5 60

10

20

30

40

50

60

70


Pres

sure

(N)

Idler number



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




4

5

6

3

2

1

1020

3040

50

150mm180mm

210mm240mm

(a)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(b)

150mm180mm

210mm240mm

4

5

6

3

2

1

2050

80110

140

(c)

4

5

6

3

2

1

4080

120160

200

150mm180mm

210mm240mm

(d)


1 2

3

4 5

6




5 Conclusions





Data Availability






Acknowledgments


References





1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89


1 2 3 4 5 60

10

20

30

40

50

60

70


Pres

sure

(N)

Idler number



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



5 Conclusions





Data Availability






Acknowledgments


References





1 60 49 54 9175 69 70 15

2 60 30 32 6775 29 32 94

3 60 7 7 075 10 11 91

4 60 9 10 1075 17 19 105

5 60 8 9 11175 14 15 67

6 60 38 40 575 51 56 89


1 2 3 4 5 60

10

20

30

40

50

60

70


Pres

sure

(N)

Idler number



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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