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Research Paper

Contact Forces in Hexagonal Idler Housing of Pipe Conveyor – A Mathematic-Statistical Evaluation

Edited by mhd on 4. Jun. 2020
The development of pipe conveyors is not yet finished. Parts with the lowest lifetime, i.e. the moving conveyor belt and the idlers are tested before the conveyor is being put into operation. The design of the supporting construction is adjusted toby practical experience and tests on various experimental rigs. Following you will find the analysis of one such test programme and the statistically relevant values.

(From the archive of ”bulk solids handling", article published in Vol. 34 (2014) No. 2 , ©2014


Fig. 1: Test rig for measuring forces in pipe conveyor belts. Photo shows the threaded rods providing the fixation of the belt sample. [5], [6] (Pictures: © Technical University of Košice / Fedorko)

Measuring of the stress-deformation relations that are occurring inside the transport belt, which is applied in the pipe conveyor, is a research subject of many developmental workplaces in the framework of the technical universities. The main reason for performing of the research activities just in this area is a fact that in spite of the several tens installed pipe conveyors worldwide the knowledge base, which is able to describe the contact force relations in the tube conveyor belt, is developed insufficiently even now. There were published various studies based on the theoretical analyses predominately, which are supported sometimes also by a computer simulation using FEM.The theoretical results create an important information base, however, taking into consideration the practical application point of view, they require also a real verification and validation. From this reason the future development of research aims to approach the reality and typical operational conditions.The measuring possibilities at the real operating pipe conveyor are very complicated [1][2]. The conveyor is usually installed in the given technological complex without a possibility to be excluded. Also, the real operational conditions of the pipe conveyor are not suitable for application of the very sensitive measuring apparatus [3].Thus, the survey effort of the researchers is oriented towards performing of their measuring experiments in the laboratories equipped with the installed special measuring and testing devices that are able to simulate the real operational conditions as close as it could be achieved [4].One of such experimental equipment was developed at the Faculty of Mining, Ecology, Process Control and Geotechnology, Technical University of Košice [5], [6] and nowadays it is exploited very effectively. This laboratory apparatus is designed so that it represents the 8 m long section of the pipe conveyor, in which the conveyor belt is transformed to the pipe form.

1. Measuring of Stress-Deformation States in the Transport Belt of the Pipe Conveyor

Measuring of the stress-deformation states was performed in order to identify the individual forces that are induced due to acting of the transport belt on the individual guiding idler rolls in three idler housings. Fig. 2 illustrates the measuring principle using the 8 m long specimen section of the pipe conveyor belt. Fig. 3 identifies the measuring points of the contact forces in the measurement places on the idler rolls of the test equipment in the hexagonal idler housings B1 to B3.

Fig. 2. Principle of the experiment performed on the 8 m section of pipe conveyor in rig. [5], [6]

The main purpose of the measuring process was to analyse and to measure forces, which are created due to packing sequence of the rubber-textile transport belt into the piped shape. This procedure is occurring not only during the pipe conveyor operation, but also in the phase of installation or replacement of the transport belt. So, no influence of the transported material was applied during the measurement.

Fig. 3: Identification of the contact forces in the measuring places on the idler rolls of the test equipment in the hexagonal idler housings B1 ÷ B3.

It is a well-known fact that determination of forces in the conveyor belt is a very difficult task also due to a fact that the belt is a hyper-elastic material with orthotropic behaviour. There are many papers in the literature dealing with this problem.This fact was relevant during selection of the points suitable for installation of the individual strain gauges. The measuring procedure was realised in several series in order to obtain the maximum amount of the measured data.

2. Measuring Process

The measuring process was realised in such way that the tightening force was increased step by step by 6000 N each up to the maximum force level of 30 000 N. The relaxing time of the belt lasted 120 seconds at the determined force level.After achievement of the maximum level the tightening force was reduced stepwise to the initial value 0 N, again using steps of 6000 N.The measurements regarding the time behayiour were repeated 10 times, which is presented in Fig. 4. The data obtained from the individual measuring were recorded continuously by means of the Labwiev software using a sampling frequency of 10 Hz. In total, up to 24 000 values of the contact forces were recorded and processed from one measurement cycle.

Fig. 4: Tension/time behaviour of the tension forces in the transport belt.

3 .Results of the Measuring Process

Information about the stress-deformation relations in the conveyor belt is an important indicator, as these relations have a direct effect on the conveyors operational factors, just as they influence the lifetime and damages of the conveyor belt. By means of their identification we can obtain relevant information from the theoretical or experimental procedures.The average values of the contact forces were calculated for the individual idler rolls during tightening and relaxing process according to the base of measured values. There were identified the maximum values of the contact forces.

  • Average contact forces in the individual idler rolls of the idler housings during tightening and relaxing of the transport belt (Fig. 5),
  • Average contact forces in the idler rolls of the three idler housing during tightening of the transport belt (Fig. 6),
  • Determination of the idler roll loadings by the average contact forces in the framework of three idler housings and in the framework of each idler housing (Table 1).
Fig. 5: Contact forces in the individual idler rolls during tightening and relaxing of the transport belt.
Fig. 6: Average contact forces in the idler rolls of the three idler housings during tightening of the conveyor belt (tightening force 18 000 N).
Idler Housing B1 B2 B3
Mesurement No. Most Least Most Least Most Least
1 ID6 ID2 ID10 & ID11 ID8 ID13 ID16
2 ID5 ID2 ID10 ID8 ID13 ID16
3 ID5 ID2 ID10 ID8 ID13 ID16
4 ID6 ID2 ID10 ID8 ID13 ID16
5 ID6 ID2 ID10 ID8 ID13 ID16
6 ID5 ID2 ID10 ID8 ID13 ID18
7 ID6 ID2 ID10 ID8 ID13 ID18
8 ID5 ID2 ID12 ID8 ID13 ID16
9 ID6 & ID5 ID2 ID12 ID8 ID13 ID16 & ID18
10 ID6 ID2 ID12 ID8 ID13 ID16

The least values of the contact forces were recorded in the overlapping area of the packed belt (idler roll ID2) and the highest increase of the contact force was observed in the bottom part of the belt (idler roll ID6). During almost all the performed measuring it was evident, which of the idler rolls was loaded maximally or minimally. The same loading of the idler rolls was monitored during measurement No. 9 in the case of the idler housings B1 and B3.There were elaborated and evaluated the following statistical values of the obtained measured data: minimum, maximum, numerical characteristics of position (arithmetic mean, median, modus), numerical characteristics of the variability (standard deviation, data dispersion), skewness and sharpness for the measured contact forces in the hexagonal idler housing (Table 2).

Idler Roll No. of Values Min [N] Max [N] Max - Min [N] Arithmetic Mean [N] Data Dispersion Standard Deviation Skewness Sharpness
ID1 100 71.91  76.41   4.50 74.14  0.84 0.73  0.10  1.95
ID2 100 16.23  20.15  3.92 18.26  0.84 0.92 0.30 -0.33
ID3 100 50.00   53.69  3.69 51.71 0.56 0.75 -0.26 0.33
ID4 100  160.08  163.37  3.29 161.77 0.52 0.72 0.19 -0.37
ID5 100  246.04  253.56  7.51 250.45   1.85 1.36 -0.88 2.17
ID6 100  183.22  188.53  5.31 186.41   1.12 1.6 -1.07 0.80 
ID7 100  11.46  15.86  4.40 13.53   0.58 0.76  0.15  1.26
ID8 100  2.66 5.39  2.73 4.5 0.41 0.64 0.25 -0.33
ID9 100  16.80 21.27  4.47 18.54   0.47 0.69  0.48 3.25 
ID10 100  46.69 50.42   3.73 48.21  0.59 0.77 0.53 -0.13
ID11 100  18.68 22.30  3.62 20.46  0.55 0.74  -0.07  -0.32 
ID12 100  59.42 62.91   3.28 61.41   0.49 0.70  -0.05  -0.12 
ID13 100  22.29 27.97 5.68 25.78 1.4 1.2 -0.76 2.73
ID14 100  18.11 22.90   3.98 20.91 0.73 0.86 -1.36 1.17
ID15 100  10.30 14.54  4.24 12.22   0.74 0.86 0.35  0.76
ID16 100  2.55 5.96  3.41 4.13   0.57 0.76 0.23  -0.37 
ID17 100  0.50 4.61   4.11 2.44   0.56 0.75  0.20 1.55 
ID18 100  -21.52 -17.85  3.68 -20.02   0.53 0.73  0.63  -0.04 

The arithmetic mean was evaluated during measuring of the stress-deformation relations in the transport belt because the measured values of the contact forces did not have the multi-peak distribution. Another reason for determination of the arithmetic mean was a fact that the individual distributions of the measured contact forces did not have open classes in the margins and the distribution was asymmetric.The next evaluated data, obtained from the measured values, is the standard deviation, which is a suitable factor for the testing statistics. The standard deviation is applied for a reliable estimation of the basic data file dispersion, which is defined as the mean square deviation in relation to the mean value.The next step was determination of the skewness, which describes symmetry of the monitored distribution of the contact force values around the mean value. The positive skewness was in the case of 11 idler rolls from the 18 investigated overall (ID1, ID2, ID4, ID7, ID8, ID9, ID10, ID15, ID16, ID17, ID18), what means that the most of the measured values are situated more left from the arithmetic mean. Seven idler rolls had the negative skewness (ID3, ID5, ID6, ID11, ID12, ID13, ID14), so these values were situated right from the mean value.The sharpness is a distribution characteristic of the contact forces values, which compares the given distribution with the normal probability distribution. Together 10 of the overall 18 id­ler rolls had the positive sharpness (ID1, ID3, ID5, ID6, ID7, ID9, ID13, ID14, ID15, ID17), what means that most of the contact force values are situated close to the mean value and the density curve is more sharp shaped than normal distribution curve. The other 8 idler rolls had the negative sharpness (ID2, ID4, ID8, ID10, ID11, ID12, ID16, ID18), thus the distribution is more uniform and its density curve is more flat in comparison to the normal distribution.

5. Concluding Remarks

It is possible to say, after statistical evaluation of the measured values that the existing relation among the tension forces and contact forces is not random in the case of the measuring realized at the idler housings B1 and B2. The fastening of the transport belt influenced the values obtained from the idler housing B3. This fact was confirmed also by the statistical evaluation. From this reason these values are not considered in the next research process.The following investigation will be oriented towards a verification of the results obtained from the experimental measurements using the computer-aided simulation. There will be determined mathematical models specified for determination of relations among the contact forces and tension forces at the forming idler rolls of the idler housings in dependence on the tension force value. Such relations offer important information for users and producers of the pipe conveyors in order to optimise their operational characteristics with regard to the motional resistances and selection of a suitable kind of the conveyor belt. Afterwards it will be possible to apply the mathematical models by means of an indirect measuring method.


This work is a part of these projects VEGA 1/0922/12 Research of effect of material characteristics and technological parameters of conveyor belts on size of contact forces and resistance to motion in pipe conveyors with experimental and simulation methods, VEGA 1/0258/14 Study of input parameter relations for interoperable transport effectivity based on mathematical model application.

A Note from the Editor

For all statements in this article that refer – directly or indirectly – to the time of publication (for example “new”, “now”, “present”, but also expressions such as “patent pending”), please keep in mind that this article was originally published in 2014.

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About the Authors
Prof. Gabriel FedorkoProfessor Gabriel Fedorko works at the Logistics Institute of industry and transport, Faculty BERG, Technical University of Kosice as Head of Logistics Institute of Industry and Transport. Within his scientific research activities he devotes himself to mod­eling and simulation of ecological transport systems.
Assoc. Prof Vieroslav MolnárAssoc. Professor Vieroslav Molnár works at the Logistics Institute of industry and transport, Faculty BERG, Technical University of Kosice as Head of Division of Transport. His research interests include the steel ropes and pipe conveyors simulated by CAD systems Catia and Creo.

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