FINITE ELEMENT ANALYSIS OF STEEL CORD CONVEYOR BELT SPLICE SONG Weigang, SHANG Wenjie, LI Xiaosen

Mechanical Engineering &Automation School of Northeastern University, Shenyang 110004, China

Key words: conveyor belt splice; finite element;

Mooney-Rivlin model

Abstract: Steel cord conveyor belt splices are connected by vulcanization. The splices are the weakest part of the conveyor. Taking type ST1250 conveyor belt splice as an example, finite element software ANSYS is used to establish the necessary model, dealing with the steel cord as elastic components and the rubber as hyper-elastic Mooney-Rivlin model. The APDL language in AYSYS is used to develop a calculation program. After analysis, the conclusion was drawn that the conveyor's vertical tension must be transferred through the shearing stress between the rubber in the splices zoom and wire rope, and the distances between the wire rope must be wide enough to ameliorate the stress condition of rubber. For the high-strength belts, due to the high density, only by increasing steps can meet this requirement.

1 Introduction

Belt conveyor is one of the most important modem bulk solid handling equipment, which is widely used in coal, electric power, metallurgy, construction materials, port and other industrial fields. With the rapid development of modem industry, belt conveyor is developing in the aspects of high speed, high power, long-distance and large conveyor. The crucial point of the belt conveyor design are the driving power and the determination of the belt intensity, and the key factor which impact the belt's strength is belt splice strength. In spite that in domestic applications of the steel cord conveyor belt, the tensile strength has achieved ST6300, but due to lack of theoretical research and practical experience in projects, a larger safety factor is used to ensure the reliability of equipments. In the actual design, usually choose 7 to 9 as safety factor, which results in excessive investment in equipment. It can be seen that improving the quality of splices is an important way to ensure reliable operation of belt conveyor and reduce equipment investment. Researches on steel cord conveyor belt splices are mainly focused on fitting process and engineering practice, while theoretical studies are relatively few. Flebbe[l) introduced the

University of Hannover's fatigue strength test system and method of steel cord conveyor belt splice, put forward the concept of dynamic safety factor, and pointed out that using dynamic safety factor method after getting the splice strength by test to choose belt type shows a better economy. Hager and Wroge(2) adopt shearing finite element model between rubber and steel cord which was advanced by Oehmen(3), to develop special program for splice design; cm corporation of the United States has developed a 3-D

finite element model(4)[5), including wire rope model,

nonlinear isotropic hyper-elastic rubber model, use

ANSYS software to calculate the result, the above two

methods are the proprietary technology of research

institutions, in the literature does not detail. Furthermore, Adams[6] under the condition that take rubber as

incompressible and non-linear material analysis the splice

use FEA.

Current theoretical research of belt conveyor splice is still

in its infancy. This paper will establish a model of all

parts of belt conveyor steel cord splice, including wire

rope, filled rubber, as well as the overall model, taking

the wire rope as the elastic components and rubber as

super-elastic components to deal with, highlighting the

characteristics of the composite material. In order to

facilitate the research on the impact of the parameters,

APDL language in ANSYS is used to develop a

calculation program.

2 Characteristic parameters of steel cord

conveyor belt splice

The wire rope of steel cord conveyor belt splice region can not be directly connected. Therefore, splice region transmits draft load through the shear stress between rubber and wire rope. Main influencing factor of the splice dynamic fatigue strength include: structure of the splice, elongation of the wire rope, rubber characteristics, load on belt conveyor etc. Fig.1.a is the structure sketches of a three-step splice, Fig.1.b is main parameters of the splice. Where: d -wire rope diameter; t -wire rope spacing in belt; g -minimum distance of the rubber in splice, that is wire rope gap;L -length of one step; S -butt gap between two wire ropes; LB -length of wire rope enter the splice bending region; LS -length of

splice. In accordance with DIN 22129.4(7) standard about steel cord belt conveyor, the values of steps and minimum length Lv of vulcanized splices can be chosen in Table 1. However, theoretical calculation and field conditions etc. should also be considered to determine those values.

Tablet Minimum recommended length of conveyor belt splice

Bclt Typc Splice s teps Min s plicc length

Lvlm ST630 I 0.55

ST800 I 0.60 STIOOO I 0.60 STl250 I 0.65 STl600 2 1.05 ST2000 2 1.15 ST2500 2 1.35 ST3150 2 1.65 ST3500 3 2.35

ST4000 3 2.65 ST4500 3 2.80 ST5000 4 4.05

ST5400 4 4.45

(a) Structure sketches of 3-step splice LS

LB L L L LB S S

'\:l :::J ill:

-- � I

... ------�1 J1 :::J

(b) Fig.l.

Main parameters of splice Splice of a steel cord conveyor belt

3 Construction of splice model

3.1 Transmission of traction force on the splices

When conveyor system is in normal operation, axial force on it is totally suffered by the paralleled wire rope. However, in direction loads are taken to establish rubber and wire rope solid model.

2

the joint part of the conveyor belt, because the wire ropes are not connected together, the axial force of the conveyor will be transmitted by the shearing force between the rubber in splices and the wire rope. The tensile stress of the wire rope can be considered as the result of a succession of shearing force acting on its surface. In Fig.2, shearing force can be used to describe the friction force transmitted between different wire ropes. If the forces acted on two adjacent unloaded wire ropes lying in the rubber are in different directions, the rubber will perform shear deformation, with the largest shear angle in the nearest region of the two wire ropes. After loading on the wire ropes, they will elongate along different directions. Elongation in axial direction is not constant value. Deformation descends from the largest stress point to the small stress point. The shearing stress of the rubber also changes along axial direction. In the region of relatively large displacement, the shear angle is the largest. The largest shear angle occurs on the two ends, while the value in the center is the smallest.

elogalloll of cord tmder load shem· defonnulion

Fig.2. Defonnation of rubber in the spacing between cords

3.2 Construction of finite element model

3.2.1 Solid model

Choose the relevant parameters of type STl2S0 conveyor belt to create a model, its parameters including: axial tensile strength is 12S0N/mm, wire rope maximum diameter is 4.Smm, spacing between wire ropes is 12 mm, belt thickness is 17mm, top cover and pulley cover is 6mm, conveyor belt weight is 24.7kg/m2. As the model structure and the load is symmetry, so only one half of the model was built for analysis. 2 wire ropes of the type STl2S0 conveyor belt joint region which are SOmm long and suffered different

3.2.2 Selection of element type

SOLID45 is taken as wire rope element, which has plasticity, creep, swelling, stress stiffness, large deformation and large strain properties. SOLIDl85 is taken as rubber element, which has super-elasticity, stress stiffness, creep, large deformation and large strain properties. Element SOLID185 can easily achieve the 2 parameters Mooney-Rivlin model.

3.2.3 Contact area of the wire rope and rubber

The strength of steel cord conveyor belt splice mainly depends on the adhesion force between the wire rope and rubber. The adhesion force is usually given by the pull out force, that is, the force to pull out unit length steel cord which is stick into the rubber. The strength of steel cord conveyor belt splice should meet the condition that the pull out force is larger than the fracture force of the wire rope. In this case, the wire rope will not be pulled out of the rubber even if it is fracture. The KEYOPT(l2) of the contact element is 5, which is fastened contact mode, with contact integral point in the sphere region in the initial and when contacted it is fastened to the target face along the normal and tangential directions. To sum up, the contact elements formed are as Fig.3.

Fig.3. Elements of contact pair

3.2.4 Imposed load

J\N

Impose the load on the element nodes. Tension suffered by the conveyor belt is much greater than its gravity, so the load is imposed neglect of its gravity. Because of taking into account the symmetry of the model, choose all the nodes on XZ plane, using DSYM command to give symmetric constraints. It can be seen from the model figure the load condition. Due to the complexity of the load, the DOF constraints are imposed, and the rigid displacement of the model is cancelled at the time. In normal operation, the elongation of the steel cord conveyor belt is about 0.2%. So when limit the elongation of one end, impose 0.3%

3

elongation on the other end. The model after being imposed load is shown in Fig. 4:

FigA. DOF constrain of model

J\N

4 Solution with FEM and results analysis

Model of the conveyor belt splice has large deformation and non-linear contact state, so nonlinear options should be set. Set time, automatic time stepping and load step option, then use the SOLVE command to solve. Fig.5 shows the Von Mises stress of the wire ropes and rubber. A program developed with APDL to take the parameters that affect results into account. The discussion of the results is as below:

TII'IE"lOO

SEQV (AVG)

DHX =.J..HE-03

STEP=l

SV!I =8

Tun;zzoo

SEQV (AUG)

DMX =.1.52:£-03

SmII' "122:51

3m "'21.413.1

1229 48685

24957 72413

AN

AN

96141 143597 191053

119869 167325 214781

Fig.5. Von Mises stress diagram of steel cord and rubber

All the parameters used in the model are the diameter of wire rope d, wire rope spacing g, and the thickness of conveyor belt h, the length selected in the model I. Through the analysis, the force of the rubber in the top and pulley cover adhesive region is smaller than that in the core region; h and 1 affect the rubber little; and at the same time this case is the analysis of one kind of conveyor belt, then the d value is constant. Keep the other parameters unchanged and make the spacing of wire ropes change from O.Olm to 0.03m with the 0.002m intervals , at the same time without losing the generality,

increase the load to make the elongation from 0.1 % to 0.4% with the step 0.001, then calculate these 11 different values respectively. Table 2 lists the Von Mises stress value by the changing the spacing of wire ropes under different loads. Figure 6 shows the curve of Von Mises stress at different load conditions with increase of the steel wire rope spacing. It is obviously that in the same load condition, the equivalent stress at the nodes decreases as width of g increasing. It makes the improvement of the force condition of rubber possible; the method is to make spacing of wire ropes big enough to reduce the stress of rubber.

Table2 Values of Von Mises stress on different loads

g/mm

Strcssl/(MPa)

Strcss2/(MPa)

Strcss3/(MPa)

Strcss4/(MPa)

0.7

1.0 1.2

0.13893 0.10319

0.27132 0.22191

0.43618 0.37108

0.63664 0.53877

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0, 1.2 I.A

1.4

0.10397

0.21209

0.35095

0.51067

3

Fig.6. Von Mises stress curve change with wire rope spacing

on different loads

From Fig.6 it can be intuitively seen that the node's equivalent stress always decreases with g increasing and changes more obviously when g is before the value of 0.Ol8m. When g is greater than 0.Ol8m the change becomes smoothly, that is, when the distance between the wire ropes is greater than 0.Ol8m it is of little helpful for improving the load condition of the rubber, so it is meaningless to continue to increase the width of the wire ropes. And by the effects of the width of conveyor belt, the rubber should be left wide enough to achieve protective effect, but it is impossible to make spacing between wire ropes greater. Fig.7 is the Von Mises stress curves when d is given

4

1.6 1.8 2.0 2.2 2.4

0.068108 0.036749 0.037487 0.038177 0.035711

0.17252 0.11108 0.10956 0.10963 0.10375

0.29927 0.21777 0.21035 0.20744 0.19636

0.43799 0.34124 0.32583 0.31890 0.30008

different values. As can be seen from the figure, Von Mises stress in the rubber decreases as the spacing between wire

ropes increasing, and the reduction trend of the stress slows

down along the direction of g increasing. By comparing,

with the diameter of the wire ropes increasing, this slowing

down trend point moves to the direction of g increasing.

We can see that in the production of connectors, the width of

the rubber between the wire ropes should be greater than a

certain value, in order to ensure a more satisfactory load

state of the rubber avoiding fatigue failure of the rubber

under too large stress. So the use of high-strength conveyor

belt in the form of multi-step connections is required. It

accords with the empirical formula of the minimum value of

the rubber width between wire ropes given by Nordell and

others, that is[51: g=0.10xd+1.5 ( 1)

where: d �-wire rope diameter. With the vertical tensile strength of the conveyor belt increasing, the diameter of wire ropes also increases correspondingly. However, the spacing between wire ropes are getting smaller, that is, the density of steel wire ropes is increasing. So if a certain width of rubber between the wire ropes is necessary, the width of the splices region is greater than the non-connected region of the conveyor belt, which is not allowed. This problem will be solved well using stepping form on the splices. As with the steps of the splices

mcreasmg, the number of splices in the WIre ropes will decrease correspondingly. So as a result of a reduction of the number of wire ropes, we can insure sufficient width of rubber.

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(a) d =5.0mm

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1.6 1.8 2 2.2 2.4 2.6 2.8 "\vire rope spacing Imm

(b) d =6.0mm

3 3.2 3.4

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,""ire rope spacing Imm

0.55

O.

0.45

0.4

35

1.3

25

(c) d =8.6mm

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0.2 L-----:--':::-----:--':::-_:!:------:::-'::------:::'-:------:::-':::-_::-':::-_--:!:-_-:::"::-==;") 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 \vire rope spacing Imm

5

(d) d =9.lmm Fig.7 Under different diameter wire rope with WIre rope

spacing changes Von Mises stress curves

5 Discussion on the division of splice steps

It is known by calculation: the number of wire rope in one-step splice region is 100% more than it in conveyor belt; in two-step splice region 50% more; in three-step splice region 33.3% more. Take one belt, the width of which is 2000mm. Suppose its width is B , the number of wire rope is n, the diameter of wire rope is d, the width of rubber between wire ropes is g in splice region. When the splice type IS one-step, the splice width of conveyor belt is:

B = 2nd +(2n-l)g + 2a ( 2) where: a --distance between the most lateral wire rope and the edge of conveyor belt. Thus:

B-2nd g< 2n-l

( 3)

When the type of conveyor belt is ST 1000, n =159, d =4.0, it is known by calculation that the value of g must less than 2.3mm, meanwhile, according to the formula (1), it is known that the minimum value of g is 1.9mm. So the splice of conveyor belt S T 1 000 can take one-step splice. When the type of conveyor belt is ST 1250, n =159, d =4.5, it is known by calculation that the value of g must less than 1.8mm, meanwhile, according to the formula (1), it is known that the minimum value of g is 2.49mm. So the splice of conveyor belt STl250 cannot take one-step splice, but instead, it should be considered another splice type, the step of which is higher. When the splice type IS two-step, the splice width of conveyor belt is:

Thus:

B = 1.5nd +(l.5n-l)g + 2a

B-1.5nd g< ----

l.5n -1

(4)

(5)

Recalculate conveyor belt STl250, at the moment, g must less than 3.9mm, it meets the requirement of formula (1). It is known by calculation that conveyor belt STl600, STl200 and STl250 meet the design requirement of the two-step splice, so they can take the two-step splice. When the type of conveyor belt is ST 3150, according to the formula (5), it is known that g must less than 2.33mm, according to the formula (1), the minimum value of g is 2.3lmm. At the moment, the distance between the most lateral wire rope and the edge of conveyor belt is 1.8mm. The rubber at the edge

of conveyor belt is too little, and it is unfavorable for the production of splice and the safe operation of conveyor belt, therefore it should take the three-step splice. When the splice type is three-step, the splice width of conveyor belt is:

Thus:

B = 1.333nd + (l.333n -l)g + 2a

B-1.333nd g< ----1.333n -1

( 6)

(7)

Recalculate conveyor belt ST3150, at the moment, g must less than 3.2mm, it meets the design requirement of the three-step splice. It is known by calculation that conveyor belt ST4000, ST4500 and ST50000 also meet the design requirement, so they can take the three-step splice. From this, it can be seen that the splice type is related to the value of t / d , with the decrease of the value of t / d , the splice type changes from one-step to three-step. So, when the type of conveyor belt is ST 5000 or higher strength, because the value of t / d is decreasing, it should take the four-step splice.

6 Conclusion

This paper analysis steel cord conveyor belt splice with ANSYS finite element software to obtain the factors that affect the splices strength and then discusses the best form of connection. The major conclusions as following: (1) On the discussion of the distance between wire ropes in the splice, we conclude that the distance should be big enough, to improve the rubber in which the force. For the high-strength conveyor belt, the only way to meet this requirement is to increase the steps of the splice to reduce the quantity of the wire rope. The higher the tensile strength of the belt, the more steps of the splice. (2) In multi-step splices, the distance between connection surface of wire ropes effects the stress of the rubber between them. The greater the distance, the smaller the stress value, but this decrease becomes less obvious when the distance between the surfaces is more than 50mm.

6

(3) The length of each step of the splices and the stress of rubber also have similar relationship, so we can increase the length of the step to reduce the stress of the rubber. But the length of wire rope is limited by its fracture force, so it is not unlimited increase in the length of splices to increase their strength.

Acknowledgements

This project is supported by National Natural Science Foundation of China (Grant No. 50775031).

References

[1 ]H. Flebbe. Dynamic splice strength--Design criterion for conveyor belts[1]. Bulk Solids Handling, 1988,8(5): 581-585 [2]M.Hager,H.von der Wroge. Design of Steel Cord Conveyor Belt Splices[J].Bulk Solids Handing, 1991, 11(4): 849-860. [3]Klaus Heiner Oehmen. Zur Berechnung zusatalicher Dehnungen in Stahlseigurten infolge Kurvenfuhrungen und Muldungsuberggangen[J],Braunkohle, 1977(6): 235�246 [4]L.Nordell,X.Qiu,V.Sethi. Belt Conveyor Steel Cord Splice Analysis Using Finite Element Methods [J].Bulk Solid Handling, 1991, 11(4): 863-868. [5]L.Nordell. Steel Cord Belt and Splice Construction[J]. Bulk Solids Handing, 1993, 13(1): 685-694. [6]A. D. Adams. FEA of steel cable conveyor belt splices [1], Rubber World, 1994, 41(9): 524-529. [7]DIN22129 Teil 4-1991. Steel cord conveyor belts use in underground coal mmmg; belt joints; dimension, requirements: Beuth Verlag 1991.