Measurement 94 (2016) 364–371
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Measurement journal homepage: www.elsevier.com/locate/measurement
Online monitoring of a pipe conveyor. Part I: Measurement and analysis of selected operational parameters Vieroslav Molnár a,⇑, Gabriel Fedorko a, Miriam Andrejiová b, Anna Grincˇová c, Peter Michalik d a
Technical University of Kosice, Park Komenskeho 14, 042 00 Kosice, Slovak Republic Faculty of Mechanical Engineering, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovak Republic c Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovak Republic d Faculty of Manufacturing Technologies of Technical University in Kosice with a seat in Presov, Bayerova 1, 080 01 Presov, Slovak Republic b
a r t i c l e
i n f o
Article history: Received 23 July 2016 Received in revised form 12 August 2016 Accepted 13 August 2016 Available online 13 August 2016 Keywords: Contact force Rubber-textile conveyor belt Idler roll Regression models Pipe conveyor
a b s t r a c t The need to maximize the performance and operational reliability of ecological continuous conveyor systems is increasing nowadays and their requirements are difficult to fulfil. One of the main reasons to this is the complexity of ecological continuous conveyor systems. Regular tracking and monitoring of systems selected parameters and indicators support their proper functioning and operational reliability. However, the process becomes useless if the parameters are not tracked and evaluated. The paper shall present the results of research aimed at determination of evaluation criteria for selected parameters. The research was carried out by a method of experimental measurement on an experimental rig the construction of which is similar to the construction of real pipe conveyors used in practice. Some of the convenient parameters to be tracked on a tube conveyor are a tension force and contact forces on hexagonal idler housing. The paper aims to track the course of contact forces and their mutual relations with intensity of tension forces. In order to create a comprehensive evaluation and analysis of the research, the experimental measurements were carried out for two cases, with and without material. The experimental tests are evaluated with the use of basic mathematical and statistics methods. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Conveyor units represent a very important part within majority of logistic systems. Their role is to transport variety of materials and foster the functioning of individual technological processes. Their reliable operation, maintenance and execution of decisionmaking processes depend on operational parameters monitoring as well as their evaluation [1]. Due to this, various reports and reviews can be produced [2] or the operation can be controlled based on the obtained parameters [3]. The kind and extent of the tracked parameters depend on many factors. Every conveyor system has its specifications and requirements. The most complicated conveyor systems, with regard to tracked parameters, are the ones that contain conveyor belts. Monitoring of conveyor belts’ operation is the key condition for their effective and reliable functioning [4]. Because of this, the issue has been much researched along with the development in various fields of technologies suitable for monitoring purposes. The research of monitoring and controlling system for conveyor ⇑ Corresponding author. E-mail address:
[email protected] (V. Molnár). http://dx.doi.org/10.1016/j.measurement.2016.08.018 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.
belts was conducted by Wang et al. [5]. They came to a conclusion that monitoring and controlling system can significantly contribute to reduction of physical work and reduction of number of accidents. The importance of conveyor belts monitoring is also supported by its necessity in various fields of industry. One of them is the mining industry where conveyors play an important role. The research of monitoring system for conveyor belts in coal mines had been carried out by Wang and Zhigang [6]. The main idea of the designed system is based on the monitoring of the drive unit operation. The other research on monitoring system design of conveyors in coal mines can be found in [7]. Designed and above mentioned monitoring systems allow tracking of a single or several parameters. One of these are the parameters of material handling as presented in his work by Li et al. [8]. One of the options of tracking the operation of conveyor belts is presented by Pang and Lodewijks [9]. They suggest the application of RFID technology and its implementation in supporting rollers. The other possible way of operational conditions monitoring is suggested by Min [10]. In his work, developing of security system for conveyor belt using the steel-cord type of conveyor is being described. Lee and Au [11] proposed a new conveyor system called
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mobile conveyor lines that can autonomously configure itself to move objects to a given destination. The above presented information shows that most attention is given to classical conveyor belts in the field of continuous conveyor systems monitoring. In practice, more often used are also different types of continuous conveyors typically derived from the construction of a classical one. These also include pipe conveyors. Pipe conveyors, in spite of their 40 years of existence, started to be more significant in the industry in the last 15 years [12]. Their development was much stimulated by increased requirements for ecological aspects in material transport. Due to this, the research of their operational needs and issues increases, too. The initial assumption that all the knowledge about classical conveyors can be applied to pipe conveyors, too, is no longer true these days [13]. Several methods of information collecting for the research of pipe conveyors are being used nowadays. Abbaszadeh et al. [14] employed the use of ultrasonic metrotomography method to research the behaviour of steel-cord conveyor. The method was chosen due to its not destructive character of analysis and possibility to identify various unwanted conditions of a conveyor, e.g. voids. The other not destructive option of analysis of rubbertextile pipe conveyors is the use of computer metrotomography method [15]. Besides the research of conveyor behaviour, the other aspects of pipe conveyors are being questioned, too. To answer the questions, various special testing devices are employed. Their specs and use are subject to several works [16–18]. Guo et al. [19] researched the optimization and experimental study of transport section lateral pressure of pipe belt conveyor. Wang et al. [20] researched the magnetic model of low resistance permanent magnet pipe belt conveyor. Mathaba and Xia [21] presented a generic optimization model for the energy management of downhill conveyors. From the information presented, pipe conveyors are widely used means of continuous material transport. Compared with the classical conveyors, the aspects of their operation are not that much researched nowadays. However, their further employment implies the need to do so. The article thus aims to depict the issues of safety system in the operation of pipe conveyors with more detailed principles and background. The issues have not been solved and published in such a complex way so far.
2. Material and methods It is not easy to identify the adverse conditions and processes in the pipe conveyors’ operation. The reason to this is their numerous occurrence in various places of the pipe conveyor track. From the point of view of absolute position, the place of their occurrence can be static, or it can eventually change depending on transport speed and time. Adverse condition occurring in a static state is commonly attributed to static parts of a pipe conveyor such as hexagonal idler housing, guiding or supporting rollers, eventually, the overall construction of the track. In case of adverse condition occurrence its position does not change, however, its further progress can occur depending on the kind of adverse condition itself. The easiest way to identify the state like this is the use of visual method when failure is directly identified (Fig. 1), respectively the indirect acoustic method can be employed. Then the adverse condition is indicated by a various intensity sound and its location must be additionally specified. In case of adverse condition with its location changing cyclically, the situation gets much more complicated since this type of adverse condition is connected with the conveyor itself, regardless to its type, either rubber-textile or steel-cord one.
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Fig. 1. The example of adverse operational condition – supporting roller missing.
Firstly, the existence of an adverse condition must be identified. In such a case, the use of visual methods has its limits for the conditions occurring in the upper layers of the conveyor belt. However, many defects occur in the inner structures of the conveyor belt where the visual methods of inspecting are not effective. At this point, further options arise but these might also have a few limits, e.g. acoustic method, thermal imaging method (Fig. 2) or a different type of non-destructive testing (NDT) method. The use of acoustic method does not seem to be effective. Although it signals the adverse condition, its location is problematic or even impossible. On the other hand, the use of thermal imagining is more effective. The most effective in such a case, however, seems to be the employment of NDT method with the possibility of conveyor’s inner structure visualisation. Execution of such a method is still costly and demanding thus not economically justified for common operational conditions. In the end, the application of the above mentioned methods is demanding and sometimes hard to execute in the course of real operation. The main reason to this is the need to record and evaluate the adverse condition at its initial stage. The sooner it happens, the faster the adequate measures can be taken to eliminate and prevent the threats to operational safety of the conveyor system. The use of online monitoring of adverse conditions in the real operation of pipe conveyor seems to be much more effective with the employment of measuring of selected values. A wide variety of parameters can be tracked like this. e.g. Checking of conveyor belt rotation (Fig. 3) and preventing the material dumping. The advantage of online monitoring is its continuous, resp. short intervals character. Thanks to this the adverse condition in the conveyor unit is reported immediately and the operator receives the info in no time. However, in order to perform the online monitoring, the parameters to be tracked and further evaluated need to be specified. The ones that will possibly be measured at minimum number of loci but will have the informative value about the adverse condition presence on the conveyor belt. The evaluation of these parameters will not only help to identify the adverse condition presence, but also decide whether it is serious one requiring a shutdown, respectively it is the one that signals the creation of an adverse condition without the need of shutdown. The parameters of such a value include tracking of tension force changes in the conveyor belt and contact force changes on the rolls of hexagonal idler housing.
3. Analysis of measurement points Dependence between the tension force and size of contact forces on individual idler rolls needs to be researched for the
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Fig. 2. The example of using of thermal imaging method.
Fig. 3. Tracking of position of overlay of a folded conveyor belt.
purpose of online monitoring. Individual measurements need to be carried out followed by their analysis and evaluation. 3.1. Tension forces TF The measurements for the purpose of online monitoring were carried out on an experimental rig derived from a real construction of a pipe conveyor. In the preparatory stage of measurement, the decision about where the measurements will take place had to be made. Based on the analysis, the decision was made. The most extensive section of the pipe conveyor is the one where the conveyor belt is folded in the shape of a pipe. The section where the belt is folded and unfolded represents just a small part of the trans-
porting track and due to the folding and unfolding processes the force ratios are extremely varied. Due to this, any results would be uncertain or even slightly misleading. In order to obtain the evaluation criteria, the point chosen was the one where the conveyor belt is relatively standstill with force ratios without many changes. We assume that at the point like this, any significant change occurs as a result of adverse or degrading condition in the conveyor belt. Due to reasons mentioned, the contact forces recorded were the ones occurring as a result of interaction between a folded conveyor belt and individual idler rolls. The measurements were done with material and without material on a conveyor belt with no damage present. The measurements were supposed to find out the effect of
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tension force change on the change of contact forces of hexagonal idler housing No. 2 as in Fig. 4. The objective was to define, on an experimental rig [22], chosen comparisons of contact forces CF with dependence on a conveyor belt sample tension with and without material, carried out by a successive increase of tension force TF to values of approximately 10,000 N (TF1), 16,000 N (TF2), 22,000 N (TF3), 28,000 N (TF4) and the increase of 6000 N. Basic numerical characteristics of obtained tension forces TF1, TF2, TF3 and TF4 are shown in Tables 1 and 2.
Table 1 Numerical characteristics of the tension force – without material. Tension force [N]
TF1
TF2
TF3
TF4
Average Maximum Minimum Standard deviation
9043.49 9120.71 8966.40 25.79
15518.42 15620.77 15417.26 34.35
21921.33 22034.02 21817.70 38.52
27743.85 27836.06 27642.46 33.96
Table 2 Numerical characteristics of the tension force – with material.
4. Results and discussion The results’ evaluation is divided into three parts: 1. Monitoring of the course of contact forces and determination of contact forces CF ratio on the rolls of idler housing No. 2 for measurements without material compared with measurements with material. 2. Determination of contact forces CF ratio on the rolls of upper section compared with the bottom section of idler housing No. 2 for measurements without and with material, separately. 3. Determination of mutual ratios of contact forces CF on the rolls of upper section and bottom section of idler housing No. 2 for measurements without and with material, separately. 4.1. Comparison of contact forces CF on the rolls The classification and location of idler rolls on idler housing No. 2 with a conveyor belt and conveyed material is shown in Fig. 5. The conveyor belt section was filled with material to 75%. From the values obtained during the measurement, the selected values were for the period of 60 s including all tension forces. The 60 s
Tension force [N]
TF1
TF2
TF3
TF4
Average Maximum Minimum Standard deviation
9079.71 9162.42 9003.95 30.07
15682.94 15788.34 15584.26 39.69
21480.46 21599.02 21374.98 44.22
27455.00 27556.46 27354.79 38.00
selection from the measurements was in more details described by Molnár et al. [17]. The average values of contact forces CF on idler rolls are shown in Tables 3 and 4. Graphical representation of recorded contact forces CF on individual idler rolls can be seen in Figs. 6 and 7. The analysis and comparison of measured contact forces of conveying without and with material shows that the courses of the forces are similar to each other, almost identical. For clarity reasons, Fig. 8 shows the graphical illustrations of the courses of measured contact forces CF on idler rolls ID11 and ID8 for tension force TF1. The difference is only in the size of measured values. Basic comparison of contact forces CF for measurement with and without material was set as a ratio of respective contact forces CF
Fig. 4. Classification and location of idler housings on an experimental rig.
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Fig. 5. Classification and location of idler rolls on idler housing No. 2 with a conveyor belt and conveyed material. Fig. 7. Measured contact forces CF – with material.
Table 3 Average values of contact forces CF – without material. Tension force [N]
ID12
ID11
ID10
ID9
ID8
ID7
TF1 TF2 TF3 TF4
130.44 197.10 230.91 249.93
59.85 109.24 140.37 157.49
103.32 163.09 198.04 217.33
50.82 81.33 103.75 119.55
14.41 26.33 36.76 45.32
36.17 58.09 79.42 96.25
Table 4 Average values of contact forces CF – with material. Tension force [N]
ID12
ID11
ID10
ID9
ID8
ID7
TF1 TF2 TF3 TF4
130.12 184.51 219.93 248.08
123.01 180.86 207.78 212.02
99.33 163.99 202.52 224.16
36.46 72.32 99.99 118.73
12.85 23.81 33.45 40.35
33.22 59.55 84.40 103.17
compared with contact force value measured without material. The results given as average are shown in Table 5. In case of position of idler roll ID11, the ratio of all contact forces is higher than 1. For tension force TF1, the value of measured contact force CFWM is double size of the value of contact force CFWOM. Table 5 implies that contact forces of almost all material impacted idler rolls related to contact forces of idler rolls without the material impact are equal to one (forces are almost identical). The only exception is the ratio of idler roll ID11 (bottom section, centre), where the values are more than one, however, they decrease with the increase of tension and converge towards one. Result like this was expected since on this idler roll, the highest load is assumed. 4.2. Comparison of contact forces CF on the idler rolls upper and bottom section The contact forces CF compared were the ones of idler rolls positions ID7, ID8, ID9 of the upper section of idler housing No. 2 with the contact forces CF on idler rolls positions ID12, ID11, ID10 of the bottom section of idler housing No. 2, which are placed one above the other. That is why the left side, the middle and the right side of idler housing No. 2 can be distinguished as in Fig. 9. The measurements were compared: – without material (WOM), – with material (WM). The resulting ratio was determined as
Z1 ¼ Fig. 6. Measured contact forces CF – without material.
RATIOðIDXÞ ¼
CFWMðIDXÞ ; for X ¼ 7; 8; 9; 10; 11; 12 CFWOMðIDXÞ
ð1Þ
where CFWOM is the contact force obtained from measurement without material for a given position of idler roll IDX. CFWM is the contact force obtained from measurement with material for a given position of idler roll IDX. The ratio shows the increase (RATIO(IDX) > 1) or decrease (RATIO(IDX) < 1) of the contact force value measured with material
CFðID12Þ ; CFðID7Þ
Z2 ¼
CFðID11Þ CFðID8Þ
and Z 3 ¼
CFðID10Þ : CFðID9Þ
ð2Þ
Due to the force of gravity and the weight of conveyed material, the values of contact forces CF in the bottom section of idler housing No. 2 are several times higher than in the upper section of idler housing No. 2. The characteristics of averages of contact forces selected ratios on idler rolls upper section to contact forces of idler rolls bottom section of idler housing are for measuring without material shown in Table 6 and for measuring with material in Table 7. On the upper section of idler housing No. 2, measured without material (Table 6), the contact forces for tension force TF1 on idler roll ID12 compared with idler roll ID7 (right side) are 3.608 times
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Fig. 8. Course of contact forces – ID11, ID8 for tension force TF1.
Table 5 Average values of contact force ratios with and without material. RATIO(IDX)
TF1
TF2
TF3
TF4
ID12 ID11 ID10 ID9 ID8 ID7
0.998 2.056 0.961 0.718 0.893 0.919
0.936 1.656 1.006 0.889 0.905 1.025
0.952 1.480 1.023 0.964 0.910 1.063
0.993 1.346 1.031 0.993 0.890 1.072
higher, however, the ratio decreases with the increase of tension force TF. For measurement with material (Table 7), the ratio is a bit higher (3.92). The same is true when comparing contact forces CF on idler rolls ID10 and ID9 (left side). On the other hand, when comparing contact forces CF of idler rolls ID11 and ID8 (middle), the ratio is much higher (4.163, resp. 9.604 for TF1). To compare,
Fig. 10 presents graphical illustration of ratios for idlers ID11 and ID8 (middle) for all tension forces TF. Tables 6 and 7 imply that the ratios of contact forces of upper section of hexagonal idler housing when compared with the bottom section, are almost identical on the left side (with and without material impact) and almost identical on the right side (with and without material impact). The exception applies to values obtained from the middle part. Without the material impact, the ratios are from 3.467 up to 4.163. With the material impact, the ratios are from 5.256 up to 9.604. 4.3. Comparison of mutual ratios of contact forces CF on idler rolls upper section and bottom section The mutual ratios of contact forces CF on idler rolls upper section and bottom section of idler housing No. 2 with material
Fig. 9. Classification of idler rolls in the idler housing No. 2.
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Fig. 10. The course of contact forces ratio of pairs of idler rolls ID11 and ID8.
Table 6 Average values of contact forces CF ratios on the upper and bottom section of idler housing No. 2 – without material. (Z)WOM
TF1
TF2
TF3
TF4
Z1 = CF(ID12)/CF(ID7) Z2 = CF(ID11)/CF(ID8) Z3 = CF(ID10)/CF(ID9)
3.608 4.163 2.034
3.394 4.152 2.006
2.908 3.820 1.909
2.593 3.476 1.818
Table 7 Average values of contact forces CF ratios on the upper and bottom section of idler housing No. 2 – with material. (Z)WM
TF1
TF2
TF3
TF4
Z1 = CF(ID12)/CF(ID7) Z2 = CF(ID11)/CF(ID8) Z3 = CF(ID10)/CF(ID9)
3.920 9.604 2.276
3.099 7.602 2.268
2.606 6.215 2.026
2.405 5.256 1.888
The graphical illustration of mutual ratios of contact forces for selected pairs of idler rolls with and without material is shown in Fig. 11. The comparison of results shows that the material impact on the size of contact forces CF on the right side of idler housing (ratios of 0.893–1.087) and on the left side of idler housing (ratios of 1.039–1.341) is not so significant. The differences between the right and left side might also be influenced by the way of conveyor belt folding. But, as expected, the ratios in the middle of idler housing are the highest (1.512–2.312). In this place, the impact of the conveyor belt as well as conveyed material is noticeable.
compared with ratios obtained without material are the values presented in Table 8. The mutual ratio is determined as
RATIOðY i Þ ¼
RATIOðZ i ÞWM ; RATIOðZ i ÞWOM
for i ¼ 1; 2; 3;
where Z 1 ¼
CFðID12Þ ; CFðID7Þ
CFðID11Þ CFðID8Þ
Z2 ¼
ð3Þ
and Z 3 ¼
CFðID10Þ : CFðID9Þ
Table 8 Average values of mutual ratios of contact forces CF with and without material. RATIO(Yi)
TF1
TF2
TF3
TF4
Y1 = CF(ID12)/CF(ID7) Y2 = CF(ID11)/CF(ID8) Y3 = CF(ID10)/CF(ID9)
1.087 2.312 1.341
0.913 1.832 1.131
0.893 1.628 1.061
0.926 1.512 1.039
Fig. 11. Mutual ratios of contact forces of selected pairs of idler rolls with and without material.
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5. Conclusions The process of online monitoring of a continuous pipe conveyor operation is difficult to perform. Its reliable operation and informative value require tracking of suitable indicators and parameters. The wide variety of parameters available, the effective ones to be used are he changes of contact forces on idler rolls of hexagonal idler housing. The changes of contact forces are mostly triggered by possible changes occurring in the conveyor belt. These include various destructive processes and irreversible changes which can, in the end, significantly impact proper functioning of the whole conveyor system. The results of experimental measurements confirm that contact forces are suitable ones to measure. The comparison of conveying with and without material confirms the initial assumption which claims that the material itself impacts the size of contact forces CF of idler rolls in bottom section of idler housing, where the forces measured are several times higher. On the other hand, we can claim that when conveying without material the courses of measured contact forces CF are almost identical. This way the option for further measurements seems to bet the employment of data transformation with the use of standardization, where the results will not be affected by various values of tension and contact forces. This finding is significant for online monitoring needs and on its basis, the measurement standards can be designed for online monitoring execution. Acknowledgements This work is a part of these projects VEGA 1/0258/14, VEGA 1/0619/15, VEGA 1/0063/16, KEGA 006STU-4/2015, KEGA 018TUKE-4/2016.
[5]
[6] [7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
References [1] T. Nowakowski, A. Tubis, S. Werbin´ska-Wojciechowska, Theory and Engineering of Complex Systems and Dependability, Springer International Publishing, Cham, 2015.
(accessed May 7, 2016). [2] X. Liao, Y. Yan, L. Wang, Z. Zhu, The design and implementation of logistics monitoring system on food safety, in: Logistics, American Society of Civil Engineers, 2009, pp. 2206–2212. . [3] A. Permala, K. Rantasila, E. Pilli-Sihvola, J. Scholliers, Monitoring models for logistics, in: 19th Intell. Transp. Syst. World Congr. ITS 2012, Intelligent Transportation Society of America, 2012. p. AP-00330 . [4] H. Wang, J.X. Dai, Research on the reliability of underground coal mine belt conveyor system, in: 2011 2nd Int. Conf. Mech. Autom. Control Eng.
[19]
[20] [21]
[22]
371
MACE 2011 – Proc., 2011, pp. 7636–7639, http://dx.doi.org/10.1109/MACE.2011. 5988818. S. Wang, W. Guo, W. Wen, R. Chen, T. Li, F. Fang, Research on belt conveyor monitoring and control system, in: Commun. Comput. Inf. Sci., 2010, pp. 334– 339. doi:10.1007/978-3-642-16336-4_44. Li Wang, Li Zhigang, Research on control system of belt conveyor in coal mine, in: Lect. Notes Electr. Eng, 2012, pp. 885–891. X. Bo, Design of monitoring software of belt conveyor of coal mine, Ind. Mine Autom. 38 (2012) 98–100. . W. Li, Z. Pang, H. Zhang, G. Meng, Design of multi-loading control system for belt conveyor, in: 2010 Int. Conf. E-Product E-Service E-Entertainment, ICEEE2010, 2010. Y. Pang, G. Lodewijks, The application of RFID technology in large-scale dry bulk material transport system monitoring, in: EESMS 2011–2011 IEEE Work. Environ. Energy, Struct. Monit. Syst. Proc., 2011, pp. 5–9. H. Min, Research on the working condition monitoring and protecting system for mine belt conveyor, Appl. Mech. Mater. 58–60 (2011) 518–523, http://dx. doi.org/10.4028/www.scientific.net/AMM.58-60.518. D. Lee, T.-C. Au, Automatic configuration of mobile conveyor lines, in: Int. Conf. Robot. Autom., IEEE, Stockholm, 2016, pp. 3841–3846, http://dx.doi.org/ 10.1109/ICRA.2016.7487572. S. Hötte, L. Overmeyer, T. Wennekamp, S. Hotte, Research on the form force behaviour of a pipe conveyor in different curve radii, Bulk Solids India 2011 (2011). Y. Pang, G. Lodewijks, Pipe belt conveyor statics – comparison of simulation results and measurements, Bulk Solids Handl. 33 (2013) 52–56. . J. Abbaszadeh, H.A. Rahim, R.A. Rahim, S. Sarafi, M. Nor Ayob, M. Faramarzi, Design procedure of ultrasonic tomography system with steel pipe conveyor, Sens. Actuators, A Phys. 203 (2013) 215–224. G. Fedorko, V. Molnár, J. Zˇivcˇák, M. Dovica, N. Husáková, Metrotomography – a progressive method for conveyor belt analysis, Bulk Solids Handl. 33 (2013) 56–60. P. Michalik, V. Molnar, G. Fedorko, M. Weiszer, An experimental test rig for measuring the strength of pipe conveyor belts, Bulk Solids Handl. 33 (2013) 52–55. V. Molnár, G. Fedorko, M. Andrejiová, A. Grincˇová, M. Tomašková, Analysis of influence of conveyor belt overhang and cranking on pipe conveyor operational characteristics, Meas. J. Int. Meas. Confed. 63 (2015) 168–175, http://dx.doi.org/10.1016/j.measurement.2014.12.013. M.E. Zamiralova, G. Lodewijks, Measurement of a pipe belt conveyor contact forces and cross section deformation by means of the six-point pipe belt stiffness testing device, Measurement (2015), http://dx.doi.org/10.1016/j. measurement.2015.03.045. Y. Guo, S. Wang, K. Hu, D. Li, Optimization and experimental study of transport section lateral pressure of pipe belt conveyor, Adv. Powder Technol. (2016), http://dx.doi.org/10.1016/j.apt.2016.04.026. S. Wang, D. Li, Y. Guo, Research on magnetic model of low resistance permanent magnet pipe belt conveyor, 3D Res. 7 (2016). T. Mathaba, X. Xia, Optimal and energy efficient operation of conveyor belt systems with downhill conveyors, Energy Effic. (2016), http://dx.doi.org/ 10.1007/s12053-016-9461-8. V. Molnár, G. Fedorko, M. Andrejiová, A. Grincˇová, M. Kopas, Monitoring of dependences and ratios of normal contact forces on hexagonal idler housings of the pipe conveyor, Meas. J. Int. Meas. Confed. 64 (2015) 168–176, http://dx. doi.org/10.1016/j.measurement.2014.12.055.