The tube chain conveyor is used exclusively for the transport of bulk solids and ... parison with belt feeders, trough chain conveyors, screw conveyors and bucket ...
EXPERIMENTAL TESTS AND DESIGN OF TUBE CHAIN CONVEYORS S. Schmolke, A. Katterfeld, F.Krause Institut für Förder- und Baumaschinentechnik, Stahlbau und Logistik (IFSL) Otto-von-Guericke-Universität Magdeburg Universitätsplatz 2 39106 Magdeburg
Summary This paper describes the first results of experimental tests of tube chain conveyors. Tube chain conveyors are to handle bulk material. Up to now there was no research work in this area. The aim of the research work is to get the first scientific principles for calculating and design such systems. A pilot plant was installed and new methods for data transmitting out of a closed metallic sealed system were developed. Extensive measurements with different bulk solids were done and new results could be collected. The results of the theoretical entries for calculating and design such conveyors were compared with the experimental results.
1
NOMENCLATURE Ai dRi IV Fq FKv FRh Fv Fz1 Fzv g H lTS nF px pz qF qKS t TK VF Vi VKS vK x, y, z ηV ηI λ λa , λp µK µW ρ ϕe
Sectional area inside the tube Inside diameter Volumetric flow Inertial force of weight per meter of chain and disks Motion resistance because lift of chain and disks in vertical parts Motion resistance because friction of chain and disks in horizontal parts Total motion resistance in vertical parts Total force because weight and friction of bulk solid acting of one disk in vertical parts Total force acting of all disks in vertical parts Acceleration of gravity Total height of vertical parts Disk pitch Number of bulk solid parts between disks Horizontal pressure Vertikal pressure Weight per meter of bulk solid Weight per meter of chain with disks Chain pitch Chain tractive force Volume, eq. (3) Volume inside the tube Volume of chain with disks Chain speed Coordinates Volumetric efficiency Capacity efficiency Rankine coefficient Rankine coeff. of active/passive limit rate in accordance with Rankine’s theory Friction coefficient chain/tube Friction coefficient bulk solid/tube Density of bulk solid Angle of internal friction
m² m m³/s N N N N N N m/s² m m N/m² N/m² N/m N/m m N m³ m³ m³ m/s m
kg/m³ rad
2
INTRODUCTION
The tube chain conveyor is used exclusively for the transport of bulk solids and belongs to the mechanical continuous conveyor group with circulating train means. The quite old conveyor technology working on the damming up disks principle was promoted by the use of new materials and new chain designs since 1970. First of all Remmer Schrage and his company Schrage Rohrkettensysteme GmbH have been contributing to this development. Due to this facts the tube chain conveyor is a continuous conveyor with many advantages in comparison with belt feeders, trough chain conveyors, screw conveyors and bucket chain conveyors. While with most mechanical continuous conveyors only a straight conveying direction is possible, changes in the conveying direction, whether they are three dimensional or flat, are no problem with a tube chain conveyor. Also dust,-gas- and pressure-tightness is easy to realize. Another advantages is the possibility to work in difficult environments. Temperatures about 300°C and the transportation of abrasive bulk solids can be managed. Nevertheless tube chain conveyors have a lower power consumption then e.g. screw conveyors. At this reason tube chain conveyors serve the protection of the environment and that of man. Up to now the design of tube chain conveyors bases only on the practical experiences of few people. However some conveyors were damaged at work. Typical reasons for trouble with such conveyors are chain breaks or breaks of transportation disks as shown in figure 1.
a b Figure1: a) Abrasion on a chain link causes change of chain pitch and defect of conveyor b) double sided reversed bending fatigue crack in the weld between disk and chain Hence one of the research activities of our institute (IFSL) on the University of Magdeburg is to study the behaviour of tube chain conveyors to get the first scientific principles for calculating such systems and to prevent conveyor defects. At this reason a pilot plant has been installed to get or to improve the new methods of calculating.
3
DESIGN OF TUBE CHAIN CONVEYOR PILOT PLANT
The tube chain conveyor belongs to the mechanical continuous conveyor group with circulating train means. Figure 2 shows components of the tube chain conveyor of the pilot plant as example for a typical tube chain conveyor. The closed conveying system consists of several metallic tubes connected with standard flanges, a driving unit, a tensioning unit, a conveyor chain and depending on the line-run a tube bend. Bulk solid is conveyed in the tube by disks fixed on the chain in a definite distance as shown in figure 3. The route of the tube conveyor can be horizontally, vertically, or with an inclined orientation. A photo of the pilot plant is showed in figure 4
antenna
outlet opening
driving unit
receiver tube
redirection unit
feed opening
antennas antennas
tube bench
chain A with measurement disk
Figure 2: Pilot plant of the tube chain conveyor and the chain tractive force measurement
a Figure 3:
b a) A vertical part of an empty tube chain conveyor b) A moving chain with fixed disks transports wheat
Technical Specifications of the pilot plant: volumetric flow: horizontal length: vertical length: inside diameter: outside diameter: disk diameter:
Ivmax ≈ 20 m³/h Lh = 6 m Lv = 4 m dRi = 159 mm dRa = 168 mm dS = 148 mm
chain: chain pitch: disk pitch: velocity:
round steel link chain DIN 762-2-16×80 E (carbonized ) t = 80 mm lTS = 160 mm vK = 0.024…0.37 m/s
Figure 4 (left): Tube chain conveyor pilot plant in the bay of the IFSL university Magdeburg
0
1
drive station
2 10 3
redirection station
5
6
4 9
7
8
Figure 5 (below): Calculation parts of the pilot plant
4
THEORY
Up to now principles for design tube chain conveyor does not exist. Krause already wrote in [3] that the behaviour of tube chain conveyors is similar to the behaviour of scraper conveyor and through chain conveyors, because all of these conveyors have an endless train means. But there are certain differences. For example the different to the scraper conveyor is that the supporting member is closed (tube). The different to the through chain conveyor is the use of only one round steel link chain, which causes the tractive force only form-closed. At this reason the new research results and design advices, which were published especially to the through chain conveyor from Wehking [11] – Hermann [13] can not be used to calculate the design of a tube chain conveyor. The most important influence on examination tube chain conveyors have the motion resistances, which depend on the line-run of the conveyor, the properties of bulk solid and the tensile force of the chain. For an analytical description of the motion resistances the conveying (filled) site of the pilot plant can be divided in a horizontal, a vertical and a bend part. The classification of the pilot plant line-run parts is illustrated in figure 5. Besides the horizontal parts (8 filled), the bend part (9) and the vertical part (10), other parts are identified to get a better understanding for the measurement signals explained in chapter 5. The following entries for calculation a tube chain conveyor are summarized shortly. For better understanding and further explanations the articles by Krause [3]-[7] are advisable. 4.1
Volumetric Flow
The theoretical volume, which the bulk solid is able to fill up can be calculated if the volume of the chain and the transportation disks is subtracted from the volume inside the tube. The so called volumetric efficiency is given by: V − VKS VF ηV = i = (1) Vi Vi
Depending on the disk pitch and the size of chain as well as disks the volumetric efficiency is about
ηV ≈ 0.90…0.96. To calculate the real volumetric efficiency it is necessary to consider the influences of the inclination of the line run, the bulk solid density at the feed zone, the properties of the bulk solid and so on. This influences can be united in the so called capacity efficiency ηI. The real volumetric flow can be expressed as follows: I V = η I ⋅ I Vth = η I ⋅ η V ⋅ A i ⋅ v K 4.2
(2)
Motion Resistance in Horizontal Parts
By regarding the tube as a square it is possible to calculate the frictional force on the wall which is caused by bulk solid flow. For the easiest case a stress condition in accordance with Rankine’s theory can be assumed. Due to the wall friction this is actually not correct. The motion resistance in horizontal parts is given by: FRh = l ⋅ [η I ⋅ η V ⋅ ρ ⋅ g ⋅ A i ⋅ µ W ⋅ (1 + η I ⋅ η V ⋅ λ h ) + q KS ⋅ µ K ]
(3)
respectively: FRh = l ⋅ [q F ⋅ µ W ⋅ (1 + η I ⋅ η V ⋅ λ h ) + q KS ⋅ µ K ]
(4)
With following assumptions: •
d Ri ⋅ π and a stress condition of Rankine is assumed 2 Constant sectional area of the flow of bulk solid above the whole conveying route with the following material mass per meter: q F = ηI ⋅ ηV ⋅ A i ⋅ ρ ⋅ g (5)
•
For the active and passiv stress condition in accordance with Rankine’s theory is λ given by:
Square tube section with a = A i =
( (45
) / 2)
λ a = tan 2 450 − ϕ e / 2
(6)
λ p = tan
(7)
2
0
+ ϕe
4.3 Motion Resistance in Vertical Parts In vertical parts of the conveyor segments of the bulk solid flow have to lift against the wall friction. Different to the theory of Janssen the friction force on the wall has an effect on a differential small piece of bulk solid flow in the bottom direction as illustrated in figure 6. Krause showed this already in [3]. The evaluation of the equilibrium of forces and the solving of the differential equations results in the following equations:
dRi z
pz
px
dz
px
lTS
µW⋅px
A⋅ρ⋅g⋅dz pz + dpz Figure 6: Basic modell for the calculation of motion resistance because bulk solid in a one part of the bulk soild flow lTS
⋅ Fz1 = p z ⋅ A i with p z = e ⋅ v ⋅ U W
Ai ⋅ ⋅ g
4⋅µ W ⋅λ v ⋅ηI ⋅ηV ⋅l TS d Ri
d3 ⋅ ρ ⋅ g ⋅ π Fz1 = Ri ⋅ e 16 ⋅ µ W ⋅ λ v
Fzv = n Fv ⋅ Fz1 =
H ⋅ d 3Ri
⋅ v ⋅U
Ai
⋅z
-1 ,
(8)
−1 ,
⋅ρ⋅g ⋅π ⋅ e 16 ⋅ l TS ⋅ µ W ⋅ λ v
d 2Ri π respectively with q F = ⋅ ηI ⋅ ηV ⋅ ρ ⋅ g 4 Fzv
w
4⋅µ W ⋅λ v ⋅ηi ⋅ηV ⋅l TS d Ri
(9)
−1 ,
(10)
(according to eq.(5))
d Ri = H⋅qF ⋅ ⋅ e 4 ⋅ l TS ⋅ µ W ⋅ η I ⋅ η V ⋅ λ v
4⋅µ W ⋅λ v ⋅η I ⋅η V ⋅l TS d Ri
(11)
−1 .
The motion resistance due to lift of chain and disks is given by: FKv = H ⋅ q KS .
(12)
(13)
Hence the whole motion resistance results in the following equation: Fv = Fzv + FKv .
(14)
The results of the experimental test have to confirm this theoretical results. Especially the definition of the λvvalue depend on the bulk solid, the capacity efficiency ηI and the disk pitch is necessary. In addition to that it is necessary to check whether the calculation model illustrated in figure 6 is right. 4.4
Motion Resistance in a Tube Bend and any Inclined Parts
In guidance with big radius high motion resistance can be expected. Results of research for an analytical model of the effects in tube bends and any inclined conveyor parts were published by Krause in [3]-[6]. 5
EXPERIMENTAL TESTS
For the analytical description of motion resistance large-scale research is done. But the theoretical results have to be compared with the real behavior to support or to improve the entries for calculating. At this reason it is necessary to collect measurement data from certain sources. The evaluation of the certain equation which are published in this paper results that is it necessary to measure following very important data: Measurement signal
Tractive force
Mass flow Chain speed
sensor/ aim measuring device Measurement disk including: to measure Fzv (eq. 14), FRH • Strain Gage Technology, (eq. 4), µW, µK and to final • miniaturised Amplifier calculate λh and λv • miniaturised Transmitter Load cell (Strain Gage Technology) to calculate ηV and ηI Inductive transducer to calculate ηV and ηI Table 1: The most important measurement signals
The experimental ascertainment of the chain tractive force (all over the conveying route) is of special significance for the design of calculation of tube chain conveyors. Up to now it was impossible to measure tractive forces directly.
5.1
Measurement of tractive force
To measure the tractive force the measurement system has to be up to the following demands: • The tractive force has to be measured directly at the chain link. The sensor has to be resistant against high mechanical load and abrasion. • Signal conversion, amplification and power supply have to be placed right next to the chain link and move as well. • Signals of the chain tractive force have to be sent from the moving chain inside of tube to the outside by a suitable transmission technology. • Received signals of the chain tractive force are to store, to display in the form of online graphics and to condition together with other measurement signals (handling speed, volumetric flow, route of material...) using a measurement PC equipped with adequate hardware and software. Measurement - PC
Antennas 1- 6 on the plant
Measurement Disk
DIAdem analog-digital-converter DT 2812
Battery
Transmitter
Splitter
Receiver
Strain Gage
Figure 7: Block diagram of the chain tractive force’s measurement and signal transmission
Main problems consist in the application of a “chain tractive force sensor” and the signal transmission out of the closed metallic tube. This transmission means the clean transmission of measurement signals out of the Faraday screen. One chain link equipped with Strain Gage Technology. It was used a full bridge shown in figure 7 as a sensor in the way, where only the tractive force component is active and all other components are neutralised by circuitry Receiver
SG 2
U
~ ~ ~
SG 1
UB
f
Amplifier SG 3
SG 4
VHF-transmitter
Figure 8: Scheme of the strain gage (SG 1-4) application
One of the disks was prepared to be a measurement disk as illustrated in figure 9. Figure 8 shows the components of this measurement disk including the chain link with Strain Gage Technology, the miniaturised amplifier, the miniaturised VHF-transmitter, and the storage battery for power supply of all electronic components. With a special arrangement of transmission and receiver antennas it is possible to send the signal of the chain tractive force out of the tube in good quality from all over the conveying route as illustrated in figure 7.
Figure 9: Measurement Disk
5.2
Analysis of measurements
chain tractive force [kN]
6 7
6
7
8
9
8
9
10
10
0 1 2
3
0 1 2
4
3
4
5
5 0.35
5
0.3
velocity [m/s]
Measurement signals like tractive force, speed of chain and other parameters are acquired and recorded together all over the process in the computer measurement system. In Figure 10 the progression of the chain tractive force (and the speed of the chain) depending on the conveying route distance of a circulation of the chain is shown. The smoothed measurement signal shows a typical course of tractive force. The entire conveying route was divided into calculation-parts 0-10 which are similar to the calculation parts in chapter 4, figure 5.
0.25
4
0.2 3 0.15 2 0.1 1
0.05
0
0 5
0
10
15
parts
20 distance [m]
chain tractive force smooth chain tractive force velocity
Figure 10: A typical course of the chain traction force
In Part 9 a strong rise of the chain tractive force can be recognised. That is why in this part the friction between the disks and the tube bend is higher than in all other parts. A result of this effect is a high motion-resistance. On top of the vertical part 10 the chain tractive force reaches a maximum, due to the friction between bulk solid and tube and the weight of bulk solid and chain.
6
RESULTS
Extensive measurements with different bulk solids have been done. The chain tractive force in the explained systems was measured from 1 to 8 kN. These values depend on the chain stress before the measurement starts, the bulk solid properties and the filling level. The maximum value corresponds to 10% of the fraction force of the chain. In figure 11 and 12 some representative courses of measurement data of chain tractive force with different parameters were selected, to illustrate the general influence of bulk solid properties. Krause already showed in [5] the influence of chain speed and filling level. In table 2 and 3 an example for calculating the unknown parameters of behaviour of tube chain conveyors is given. In table 2 the theoretical friction coefficient µW between bulk solid and steel, determined by shear tests, can be compared with real friction coefficient inside the tube, determined by analyzing chain tractive force during transportation. The difference between these value can be explained with the roughness inside the tube. Bulk solid is deposited in the uneven tube surface and effects an friction between bulk solid and bulk solid. Hence the real friction coefficient is lower than the theoretical determined value. The λ-values, shown in table 3 were iteratively calculated using equations 4 and 12.
force [kN]
6 7
8
9
10
012
3
4
5 parts
5
tractive force wheat 90% 4 tractive force unfilled
3
2
1
0 0
20
15
10
5
distance [m]
Figure 11: Chain tractive force of one circuit with wheat (90% filling level) compared to the chain tractive force while unfilled conveyor force [kN]
6 7
8
9
10
012
3
4
5 parts
5
tractive force weath 90% 4 tractive force unfilled
3
2
1
0 5
0
15
10
20
distance [m]
Figure 12: Chain tractive force of one circuit with wheat (90% filling level) compared to the chain tractive force with flour wheat (90% filling level) and the same tension force
Table 2: Experimental gained parameters Bulk solid Wheat Flour of wheat
ρ [kg/m³] 800 586
µW theoretical against steel 0,40 0,56
Table 3: Calculated values transporting wheat ηI 0,75 0,87
λh (eq. (4)) 1,45 1,50
λv (eq. (13)) 1,08 1,42
µ W while transportation 0,33 0,38
To comparison the λa and λp –values determined on shear tests and equation 6, 7: λa = 0.32 λp = 3.12
Broken and disrupted chains are the results of extreme situations, like the cant of disks in the tube, drive-station or redirection-station. If parts of bulk solids are canting between the disks and the tube another extreme situation is possible. 7
CONCLUSION
This paper shows the good correspondence between theoretical calculated values and the measurement data from the pilot plant. Founded on the measurement data for wheat it was possible to determine the exact capacity efficiency and the real friction coefficient of one circuit. Because wheat flour has bad flow properties it was impossible to reach a constant volumetric flow for any filling level with the used bunker. It is necessary to use discharge aids. Nevertheless some tests with wheat flour were successful. Hence it was possible to compared the measurement data to show the first time the dependence of properties of bulk solids. To support the first results and entries for calculating the design of a tube chain conveyor more tests with different bulk solids, capacity efficiencies, chain speeds and disk pitches are necessary. First of all a standardized method of evaluation the measurement data is important to compare the different data. Then it is possible to asses the entries, which are published in this article. 8
ACKNOWLEDGMENTS
The authors are grateful to the pilot plant provided by Schrage Rohrkettensysteme GmbH, Friedeburg, Germany. 9
REFERENCES
[1]
SCHRAGE, F.: Einsatz von Rohrkettenförderern in der industriellen Praxis. Hebezeuge und Fördermittel, Berlin, (37) 1997, Heft 12, S. 538 – 540.
[2]
Firmenschrift Schrage Rohrkettensystem GmbH Friedeburg, 1998
[3]
KRAUSE, F.; BANSE, W.; LORZ, S.: Bewegungswiderstände und Kettenbeanspruchungen bei Stauscheibenförderern. Tagungsband Schüttgutfördertechnik, Universität Magdeburg, 1997
[4]
KRAUSE, F.; BANSE, W.; SCHMOLKE, S.; WERNER, A.: Theoretische und experimentelle Untersuchungen an Stauscheibenförderern (Rohrkettenförderern). Schüttgut 2/1999, Trans Tech Publications
[5]
KRAUSE, F.; BANSE, W.; SCHMOLKE, S.; WERNER, A.: Einfluß der Schüttguteigenschaften auf den Bewegungswiderstand von Rohrkettenförderern. Fachtagung Schüttgutfördertechnik, IFSL der Universität Magdeburg 1999.
[6]
KRAUSE, F.; BANSE, W.; SCHMOLKE, S.; WERNER, A.: Beanspruchung der Rundstahlkette von Stauscheibenförderern (Rohrkettenförderern). Fördertechnik-Tagung TU Dresden 1999.
[7]
KRAUSE, F., BANSE, W.: Der Rohrkettenförderer (Stauscheibenförderer) – ein universeller raumgängiger Förderer für viele Gutarten und kürzere Förderwege 13. Herbstschule Breslau 2000
[8]
Patent: Datenübertragung aus einer metallisch gekapselten Förderstrecke, S.Schmolke, A.Werner, PatentNr.: DE 19838831, 3/2000
[9]
SCHMOLKE, S., KATTERFELD, A.: Measurement Signals of the Chain Tractive Force from a Closed Pipe Circuit. Conference proceeding MAT 2001
[10]
SCHMOLKE, S.: Was geschieht mit der Kette im Rohr. Gesa- Symposium 1999, VDI- Berichte Nr. 1463, VDI Verlag Düsseldorf, 1999
[11]
WEHKING, K.-H.: Untersuchung zur Optimierung von horizontal arbeitenden Trogkettenförderern. Dissertation Universität Dortmund, 1986
[12]
SALLER, M.: Beitrag zur Berechnung und Optimierung senkrechter Trogkettenförderer. FortschrittBerichte VDI Reihe 13 Nr. 30, VDI Verlag Düsseldorf, 1987
[13]
HERMANN, W.: Beitrag zur optimierten Auslegung senkrechter Trogkettenförderer. Fortschritt-Berichte VDI Reihe 13 Nr. 44, VDI Verlag Düsseldorf, 1994
