Functional Analysis of Tube Chain Conveyors

Functional Analysis of Tube Chain Conveyors

Friedrich Krause, Andr� Katterfeld*(Received: 6 February 2004; in revised form: 23 April 2004; accepted: 3 May 2004)

Abstract

This paper describes some of the aspects necessary forthe design and use of tube chain conveyors. It is basedon the reports of experienced experts and recent tubechain conveyor experimental results. The aim of theresearch work is the formulation of general technicalregulations for tube chain conveyors. Theoreticalmodels were developed, which allow the calculation

of the motion resistances in all parts of the conveyor bythe use of empirical extracted correction factors.Specially designed measurement equipment enabledthe measurement of the important chain tractive forcefrom the closed tube system. The measurements showthe influence of the major operational parameters andthe bulk solid properties.

Keywords: bulk solid handling, tube chain conveyor

1 General Information about Tube ChainConveyors

The tube chain conveyor is used exclusively for thetransport of bulk solids and belongs to the mechanicalcontinuous conveyor group. Since 1970, the conveyortechnology was based on the so called „damming updisk” principle and was applied to the newmaterials andnew chain designs. The tube chain conveyor is acontinuous conveyor with many advantages when com-pared to belt feeders, trough chain conveyors, screwconveyors, and bucket elevators.Whilemostmechanicalcontinuous conveyors can only manage one straightconveying direction, tube chain conveyors can convey inall three directions. Also, these conveyors can be usedfor dust, gas-, and pressure-tight conveyor systems.Another advantage is the possibility of working indifficult environments. Temperatures up to 200 8C andthe transportation of abrasive bulk solids can beaccommodated by these conveyors. Tube chain convey-ors have a relatively low power consumption comparedto screw conveyors so are more economically efficient,which can lower the environmental burden through thisreduced power consumption. The main problems with

tube chain conveyors are the breaking of the chains and/or transportation disks, as mentioned in section 2.Hence, this research covers the scientific behavior oftube chain conveyors to calculate and prevent theseproblems.The closed conveying system of a tube chain conveyorconsists of several metallic tubes connected with stand-ard flanges, a driving unit, a tensioning unit, a conveyorchain, and a tube bend, if applicable. Bulk solid isconveyed in the tube by disks fixed on the chain as shownin Figure 1. The route of the tube conveyor can behorizontal, vertical, or inclined.

2 Typical Design Faults

After several years of research and experience withtrouble shooting tube chain conveyors, the most impor-tant design aspects are listed as follows:

* First of all, a reasonable conveyor route design is veryimportant for the smooth functioning of tube chainconveyors. Although, one of the major advantages ofthis kind of conveyor is the three dimensional convey-or routes, long conveyor routes, with many redirec-tions, can be problematic.

* To change the direction of the conveyor route it isnecessary to utilize a tube bend or a redirectionstation. A sprocket or a rim wheel (see Figure 2) canbe used for redirecting the chain for small radii. Amajor fault occurs when using a sprocket wheel while

8 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim DOI: 10.1002/ppsc.200400937

* Prof. Dr.-Ing. habil. Dr. h.c. F. Krause; Dipl.-Ing. A.Katterfeld (corresponding author), Institut fDr Fçrder- undBaumaschinentechnik, Stahlbau, Logistik, The Otto-von-Guericke-University Magdeburg, Postfach 4120, 39106 Mag-deburg (Germany).E-mail: [email protected]

348 Part. Part. Syst. Charact. 21 (2004) 348 – 355

transporting bulk solidswith a high filling level. This iscaused by the excessive abrasion between chain, bulksolid and sprocket wheel, which significantly damagesthe conveyor after a short period of time.

* High tension on the chain also causes high abrasion(see Figure 3) between the chain links, and in theworst case the chain breaks. To minimize this prob-lem, the strength of the chain lockmust be equal to theother chain links.

* The welding of the disks on the chain decreases thestrength of the steel chain, due to microstructuralchanges in the steel from the heat of the weld [2]. Thisis the main reason for conveyor defects caused bybroken disks. This problem can be reduced by usingnewly developed disks [1], which are manufacturedusing point press welding of short bolts. The newdesign of the self-blocking disksminimizes the dangerof disk-breaking.

* Depending on the tube section, there are two typicalkinds of tube chain conveyors, circular and square.Tube chain conveyors with circular sections havemore advantages in comparison with square sections.The circular disks cannotwedge or block the tube, likesquare disks can. Furthermore, it is easy to redirect thechain with circular disks using a tube bend or a rimwheel.

3 Theory

To date, general design principles for tube chain convey-ors have not been formulated in the literature. Krauseobserved that the behavior of tube chain conveyorsseems to be similar to the behavior of scraper conveyorsand trough chain conveyors, as all of these conveyorshave an endless train [3], but there are specific differ-ences. In contrast to scraper conveyors, the support forthe tube chain conveyor is closed (tube) and unliketrough chain conveyors, a tube chain conveyor uses onlya single chain with fixed transport disks to carry the bulkmaterial (only closed form). Due to these specificdifferences, recent research results and design advancesfor the general design principles for the trough chainconveyor fromWehking [4], Saller [5], and Hermann [6]cannot be applied when designing tube chain conveyors.The analysis of the motion resistances is the key todefining the power consumption of the tube chainconveyor drive as well as the design parameters for theconveyor components, e.g., chain and transportationdisks.Generally, the calculation theorymust consider theconveyor route. Based on this, a tube chain conveyor canbe divided into the following routes: horizontal, vertical,and inclined aswell as redirection sections. Furthermore,the properties of the bulk solid and the pre-tensile force

Fig. 1: Tube chain conveyor transporting wheat.

Fig. 3: High abrasion on a chain link.

Fig. 2: Rim (a) and sprocket wheel (b) [1].

349Part. Part. Syst. Charact. 21 (2004) 348 – 355

of the chain will influence the motion resistances. Withthese considerations, the following fundamental equa-tions will define the calculations required for the designof tube chain conveyors.

3.1 Volumetric Flow

If VKS is the volume of the chain and the transportationdisks and Vi is the volume of the inside tube, then thetheoretical volume to fill the bulk solid, VF, is calculatedas Vi - VKS. The maximum volumetric efficiency, hV , isgiven by:

hV ¼ Vi � VKSVi

¼ VFVi

: ð1Þ

Depending on the disk pitch and on the size of thechain and disk, the volumetric efficiency is abouthV � 0.89...0.96. For an exact calculation of the realvolumetric flow, it is necessary to consider the othermajor operational parameters, such as the inclination ofthe conveyor route, the bulk solid density at the feed zone,and the properties of the bulk solid. These parameters areused to define the capacity efficiency, hI . The realvolumetric flow, IV, can then be expressed as follows:

IV ¼ hIIVth ¼ hIhVAivK: ð2Þ

3.2 Motion Resistance in Horizontal Parts

The motion resistance, due to the friction between bulksolid and tube, can be calculated easily by assuming asquare section for the tube. Furthermore, active stressconditions are defined using Rankines theory. It shouldbe noted that these assumptions do not consider theinfluence of the sticking of the bulkmaterial between thedisks and tube and there may be other unknown stressdistributions caused by other factors (e.g., the chain issurrounded by the bulk material) that are not consid-ered. In order to better define these deficiencies acorrection value, kh, is incorporated into the model. Themeasured value is generally obtained by multiplying thetheoretical value by this factor:

FMeasured ¼ ð1þ kÞFTheory: ð3Þ

This equation can be used for the calculation of thecorrection factor in all parts of the conveyor route. Themotion resistance in horizontal parts is given by:

Fh ¼ ð1þ khÞl qFmW 1þ hIhV

la

� �þ qKSmKS

� �ð4Þ

where

qF ¼ hIhV1gAi: ð5Þ

3.3 Motion Resistance in Vertical Parts

The bulk solid segments between two transportationdisks must be vertically lifted against the wall friction.Figure 4 shows a differential bulk material element ofsuch a segment.The friction force on the wall affects the differentialelement in the downward direction, unlike in the silotheory of Janssen.Equilibriumanalysis of thedifferentialelement provides the following equation for the motionresistances in one segment:

Fv1 ¼d3Ri 1gp16mWla

e

4mWla

dRihIhV lTS � 1

!: ð6Þ

The completemotion resistance in vertical parts can thenbe calculated as the sum of the motion resistances of allsegments over the conveyor height and the gravity forceof the chain and disks. Similar to the horizontalresistance, the model does not include any assumptionsfor the sticking influence or unknown stress distributions.Therefore, a correction factor, kv, was introduced withthe corrected vertical motion defined as:

Fv ¼ ð1þ kvÞ

� HdRiqF4hIhVlTSmWla

e

4mWla

dRihIhV lTS � 1

!þHgqKS

" #:

ð7Þ

3.4 Motion Resistance in Inclined Parts

Tube chain conveyors allow the transportation ofbulk solids via inclined conveyor routes. Due to theunknown behavior of the bulk solid inside such parts,

Fig. 4: Differential element of one disk segment in vertical parts.


where the orientation of the bulk solid surface cannotbe defined analytically, the following equation forcalculating the motion resistances is given for theinclined angle, d.

Fi ¼ Fh cos dþ Fv sin d: ð8Þ

3.5 Motion Resistance in Tube Bends

High motion resistance can be expected in the redirec-tion sections with large radii. Based on EytelweinNstheory, a theoretical model was developed to calculatethe motion resistance due to the friction between thebulk material and the tube, as well as between thetransportation disks and the tube [3]. For this, thefollowing assumptions are made:

* the transport chain has a differential chain pitch, i.e.,an infinite number of disks are fixed on this chain,

* transportation disks have infinitesimal radii,* the distinct friction process is supposed to be a linefriction between the tube bend, which is reduced to itsaxis and can be imagined as a fixed support-line, andthemass allocated axis of the reduced transport chain,

* the influence of the bulk solid is reduced to causefrictional forces, acting on the chain axis.

The model developed is called the line model, due to thesimplification of the line friction.Knowing the value of the chain tractive force, FTðy0Þ, atthe beginning of the tubebend, an equilibriumanalysis of

the inclined differential bend element (as shown inFigure 6) allows the calculation of the chain tractiveforce, FTðyÞ, at any bend angle, y, for any bendinclination, a or b, respectively (shown in Figure 5).A detailed derivation of the equilibrium analysis isshown in [3], which describes the calculation of themotion resistances in empty tube bends. Therefore, themodel was extended by the newly defined bulk solidfriction force in all dimensions, dFxyzRSG. The sum ofdFRT ; dFRq, and dFxyzRSG now includes the frictionalforces caused by the transportation disks and the bulksolid.

dFRT þ dFRq ¼ dymKS� qKSr sina� cosa cosyð Þ þ FTðy0Þ½

ð9Þ

dFxyzRSG ¼ dyr siny cosadRiqF4lTSmWhIhVla

e

4mWla

dRihIhV lTS � 1

!þ

dyrqFmW 1þ hIhV

la

� �cosyþ siny sinað Þ: ð10Þ

The solution of the simplified equilibrium equations is alinear inhomogeneous differential equation, which canbe written as

Fig. 5: Mechanical model to determine the motion resistances intube bends in the general position. A transparent tube bend and atransportation chain are drawn for clarity although the model willwork with only the axis.

Fig. 6: Equilibrium analysis of the inclined differential bendelement.


dFTðyÞdy

� mKSFTðyÞ ¼ A sinyþ B cosyþ C; ð11Þ

where the abbreviations A, B, and C are given by

A ¼ rqF cosadRi4lTSmWhIhVla

e

4mWla

dRihIhV lTS � 1

" #þ rmWqF

� sina 1þ hIhV

la� �

þ rqKS cosa; ð12Þ

B ¼ rmWqF 1þ hIhV

la� �

� rqKSmKS cosa; ð13Þ

C ¼ rqKSmKS sina: ð14Þ

The solution of this differential equation (Eq. 10) resultsin the following recursive equation

FTðyÞ ¼ emKSðy�y0Þ�FTðy0Þ þ

AðmKS siny0 þ cosy0Þm2KS þ 1

þBðmKS cosy0 � siny0Þm2KS þ 1

þ CmKS

�

�AðmKS sinyþ cosyÞm2KS þ 1

þ Bðsiny� mKS cosyÞm2KS þ 1

� CmKS

: ð15Þ

In extensive tests, explained in section 4, it could bedetermined that this analytically derived model must beextended by an empirically based correction factor(Eq. 3) to fit with the measured data. Therefore, themotion resistances in tube bends are generally given by

FB ¼ 1þ 2ypkb

� �FTðyÞ: ð16Þ

4 Experimental Research

Toverify the theoretical approaches discussed above andto determine the correction factors, kh, kv, and kb, it wasnecessary to undertake an extensive series of tests in atube chain conveyor system designed to reflect antici-pated operating conditions [7].The main task of the tests involved the measurement ofthe chain tractive force with a specially designedmeasurement apparatus, which was developed bySchmolke and Werner [8]. The so called measurementdisk, shown in Figure 8, is a standard disk modified to

allow themeasurement of the chain tractive force via theenclosed metallic sealed system (Faraday screen) alongthe whole conveyor route.As themain component, shown in Figure 9, themeasure-ment disk includes a specially prepared chain link withapplied strain gauge technology (full bridge), a mini-aturized amplifier with a VHF-transmitter, a 9 V batterypower supply, and an antenna. The data was received byfour antennas and the telemetric receiver, and wascollected by a PC for measurement.

Fig. 7: 3D-CAD model of the tube chain conveyor test rig.

Fig. 8: Photo of the measurement disk.


With the help of this equipment it was possible todetermine the correction factors. Due to the significantefforts required for the test procedure it was decided torun tests with typical examples of bulks solid groups,which are characterized by:

* the cohesion: free flowing or cohesive,* the particle size: bigger or smaller than the gapbetween the tube and disks, which is around 2 mm,and

* the bulk solid density: low (<1000 kg/m3) or high(>1000 kg/m3).

Previously, only bulk solids, characterized by a low bulksolid density, were tested. Examples of such solids wereoat (non cohesive, coarse-grained, particle size ca. 3 mm)and wheat grit bran (cohesive, fine-grained, particlesize< 0.5mm).

5 Results and Discussion

The evaluation of the data collected generally shows theinfluence of the bulk solid properties, as well as theinfluence of the major design and operating parametersof the conveyor. It was generally noticed that the chainstractive force is independent of chain velocity. Theinfluence of the bulk solid properties, the filling level(capacity efficiency), and the pre-tensile force of thechain can be seen clearly by comparison of the chaintractive forces for different tests, as shown in Figure 10.In addition to the importance of the bulk solid densityand friction factors, the particle size is a very importantparameter, which significantly influences the chaintractive force. This influence can be easily visualized bycomparing the correction factors, kh.It can be easily concluded that in the case of transportingbulk solids with particles smaller than the tube-disk gap,the kh factor is independent of the filling level and can beneglected. With reference to Eq. 4, the real stressconditions in such a bulk solid are obviously equal tothe assumed active stress condition. In the case oftransporting bulk solids with particles bigger than the

gap, the kh factor increases significantly with increasingcapacity efficiency, hI . Furthermore, Figure 11 shows theinfluence of the particle shape on the variance of thecorrection factors for fivemeasurements. The variance ofthe value of kh for oat is significantly higher than forwheat grit bran. This is due to the anisotropic particleshape of oat. For the vertical sections, the comparison ofthe kv factors showed little similarity with the influencesof the parameters which define kh.For the fine-grained bulk solid, the kv factor shows anapproximately constant value of 0.4. The kv factor forcoarse-grained bulk solid increases with the capacityefficiency and reaches a maximum of more than 1. Thedifferences in the kh and kv values are because of thedown trickling of the bulk material in the gap between

Fig. 9: Schematic drawing of the equipment inside the measure-ment disk.

Fig. 10: Comparison of the chain tractive force, while trans-porting different bulk solids (vk¼ 0.3 m/s, hI ¼ 60 %).

Fig. 11: Comparison of kh values, depending on the capacityefficiency, hI , while transporting oat and wheat grit bran. Theerror bars represent the maximum and minimum of 5 tests pervalue.


the tube and disks and the non uniform distribution ofthese solids in the disk segment. This solid distributionbehavior defines the different stress conditions. Never-theless, it can be assumed that the qualitative behavior ofboth correction factors are very similar, in that theydefine the interaction of the bulk solid with the tubechain conveyor system.Surprisingly, this conclusion is not applicable for theimplementation of the kb factor.Regarding Figure 13, it can be concluded easily that thekb factors for oat and wheat grit bran are much moresimilar than for the kv or kh factors. kb for oat and wheatgrit bran decreases for increasing values of hI. Theinfluence of bulk material sticking can be neglected.Also, there is no noticeable influence of the anisotropic

particle shape on kb. Due to the complex behavior duringthe redirection of the chain and the bulk material,unknown stress distributions are expected.

6 Conclusion and Outlook

Tube chain conveyors provide efficient solutions for thetransport of small and medium mass flow rates ofcommon or challenging bulk solids in a three dimen-sional route. However, the advantages can only beexploited by the use of the correct conveyor design. Thecomplex behavior of the bulk solid interaction with theconveyor parts does not allow a simple or completelyanalytical way for calculating the major parametersrequired to design these conveyors. The empiricalcorrection factors presented offer an accurate calcula-tion of the motion resistances in any part of the chosenconveyor route for typical groups of bulk solids with alow bulk solid density. More tests with higher densitybulk materials are necessary to improve and completethe research work. Although not all bulk solids can beclassified in the presented schema, the determination ofthe exact correction factors by the completion of testscarried out with the presented technology allows for thesecure and efficient design of tube chain conveyors. Itshould be pointed out that the numerical DiscreteElement Method (DEM) can also be used to simulatethe behavior of bulk solids in such conveyors and allows abetter understanding of the complex processes inside [9],as shown in Figure 14.

7 Nomenclature

A,B,C abbreviationsAi m2 sectional area inside the tubedRi m inside diameter of the tubeFb N motion resistance in tube bends

Fig. 12: Comparison of kv values, depending on the capacityefficiency, hI , while transporting oat and wheat grit bran. Theerror bars represent the maximum and minimum of 5 tests pervalue.

Fig. 13: Comparison of kb values, depending on the capacityefficiency, hI , while transporting oat and wheat grit bran. Theerror bars represent the maximum and minimum of 5 tests pervalue.

Fig. 14: DEM simulation of a simplified tube chain conveyor.


Fh N motion resistance in horizontal partsFi N motion resistance in inclined partsdFxyzRSG N spatial friction force component due

to bulk solid friction on the tube (Figure 6)FRq N friction force component due to chain

friction on tube, which is caused by thegravity force of chain and disks (Figure 6)

FRT N friction force component due to chainfriction on tube, which is caused by theaffecting chain tractive force componentin the y-direction (Figure 6)

FT N analytically calculated motion resistancein tube bends dependent on y

Fv N motion resistance in vertical partsFv1 N motion resistance in one disk segment

of vertical partsg m/s2 acceleration of gravityH m total height of vertical partsIV m3/s volumetric flowk general correction factorkb correction factor in tube bendkh correction factor in horizontal partskv correction factor in vertical partsl m length of horizontal partslTS m sisk pitchqF N/m weight per meter of bulk solidqKS N/m weight per meter of chain with disksr m tube bend radiusVF m3 volume according to Eq. (1)Vi m3 volume inside the tubeVKS m3 volume of chain with transportation

disksvK m/s chain speedx, z M coordinatesa, b rad inclination angle of a tube bend surface

to its vertical, horizontal axisd rad inclination angle of inclined partshI capacity efficiencyhV volumetric efficiency

la active lateral pressure ratio accordingto RankineNs theory

mKS friction coefficient chain/tubemW friction coefficient bulk solid/tube1 kg/m3 density of bulk solidsx N/m2 horizontal stresssz N/m2 vertical stressfe rad angle of internal frictiony rad bend angle, polar coordinate in the line

model of tube bendsy0 rad polar start coordinate in the line model

of tube bends

8 References

[1] Firmenschrift Schrage Rohrkettensystem GmbH Friedeburg,1998.

[2] F. Krause, W. Banse, S. Lorz: BewegungswiderstQnde undKettenbeanspruchungen bei Stauscheibenfçrderern. Tagungs-band Sch)ttgutfçrdertechnik, UniversitQt Magdeburg, 1997.

[3] F. Krause, W. Banse, S. Schmolke, A. Werner: Theoretischeund experimentelle Untersuchungen an Stauscheibenfçrder-ern (Rohrkettenfçrderern). Sch)ttgut 2/1999, Trans TechPublications.

[4] K.-H. Wehking,Untersuchung zur Optimierung von horizontalarbeitenden Trogkettenfçrderern. Dissertation UniversitQtDortmund, 1986.

[5] M. Saller: Beitrag zur Berechnung und Optimierung senk-rechter Trogkettenfçrderer. Fortschritts-Berichte VDI, Reihe13 Nr. 30, VDI Verlag DDsseldorf, 1987.

[6] W. Hermann: Beitrag zur optimierten Auslegung senkrechterTrogkettenfçrderer. Fortschritts-Berichte VDI, Reihe 13 Nr.44, VDI Verlag DDsseldorf, 1994.

[7] S. Schmolke, .A. Katterfeld: Measurement Signals of theChain Tractive Force from a Closed Pipe Circuit. Conferenceproceeding MAT 2001, AMA Service GmbH, 2001.

[8] Patent: DatenDbertragung aus einer metallisch gekapseltenFçrderstrecke, S. Schmolke, A. Werner, Patent-Nr.: DE19838831, 3/2000.

[9] A. Katterfeld, F. Krause: Anwendung der Diskreten ElementeMethode in der SchDttgut-Fçrdertechnik, in: Tagungsband zurSch)ttguttagung 2003, Verlag Logisch GmbH, Magdeburg2003.


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Functional Analysis of Tube Chain Conveyors