On the strength problem in chain elements overloaded during maintenance of bio-fuel conveyor

A. Žiliukas*, S. Diliūnas**, A. Jutas***, S.V. Augutis****, R. Ramanauskas***** *Kaunas University of Technology, Kęstučio St.27, 44312 Kaunas, Lithuania, E-mail: antanas.ziliukas@ktu.lt **Kaunas University of Technology, Kęstučio St.27, 44312 Kaunas, Lithuania, E-mail: saulius.diliunas@ktu.lt ***Kaunas University of Technology, Kęstučio St.27, 44312 Kaunas, Lithuania, E-mail: audrius.jutas@ktu.lt ****Kaunas University of Technology, Studentų St. 50, 51368 Kaunas, Lithuania, E-mail: stasys.augutis@ktu.lt *****Kaunas University of Technology, Studentų St. 50, 51368 Kaunas, Lithuania, E-mail: ramunas.ramanauskas@ktu.lt


Introduction
Lithuanian power economies increasingly use different kind of wood chips as the fuel for heat energy.Small deviations in maintenance conditions of chains influence on other cases of deformations that usually are not presented in the chain maintenance guide [1].According to Environmental Performance Index (EPI) Lithuania was seven-teenth during years 2011 [2].It should be mentioned that the police categories such like effects of power economies on human health or ecosystem effects were also included in that analysis [3].
Usually, mentioned plants operate chain-scraper conveyors [4].Conveyor chains equipped with rollers are designed by DIN 8167/8168.From the chain strength point of view, there are presented investigation and possible maintenance problems that change normal operational conditions, also shorten operational time of conveyor.The question was: "What reasons do influence on chain failure?" [5].Therefore, the main aim of this investigation was to find out the reasons of possible accident.This work was carried out in three stages: 1) visual inspection of working conditions and analysis of working drawings; 2) voltage/current measurements of motor, temperature on chain joins; 3) evaluation of incidental reasons on the accidental failure.In this investigation, measurements were performed as verification for presented methodology.

Computation method
For the presented strength analysis the geometric and analytical models were created.The chain then is loaded by the following loads: 1) tensile load that comes from the own weight of chain and conveyed material; 2) transversal force coming from the distortion of chain because of possible incidental operational conditions; 3) bending moment coming from the action of transversal force.These loads were superposed on the evaluating chain members having the aim to simulate real operational conditions.Fig. 1 represents principal kinematic and computational scheme indicating some cases of incidental operation that may be separated to different levels of problem formulation Eq. (2).
In the case of damaged scrapper with parameter y max , initial conveyor width B becomes shorter and then equals B 1 and then chain parameter is Trying to describe possible situations of scrapper maintenance the following boundary conditions were used   As it could be seen from the Eq. ( 2), there are four incidental cases explaining the change in geometric parameters:

Sprockets
Case I: There is normal maintenance situation, the chain has no distortion  = 0 because scrapper isn't damaged yety max = 0; Case II: A possible situation of incidental operation, conveyor scrapper is deflected at the right,  > 0; Case III: A possible situation of incidental operation, conveyor scrapper is deflected at the left,  > 0; Case IV: This is also distortion of chain with angle  > 0 without scrapper deflection (y max = 0).This situation is possible in the case of lengthening of one chain strand because of asymmetric distribution of conveyed material.
Regarding the cases mentioned above the chain may be distorted also one may have a contact with the right or left borders of conveyor.maximal value  is possible as it may be seen in Fig. 2.
Such value depends also on deflection position c 1 accordingly chosen Roman numbers I…IX.The structural difference in chain segments was taken into account with the use of chamfer width of sprocket tooth chamfer s.In this case chain has the narrower and wider segment.The narrower segment of chain slides on sprocket tooth chamfer s and chain distortion parameter becomes B ⁄ 2 + s while the wider segment of chain slides freely on sprocket tooth and distortion parameter becomes B ⁄ 2.
As we can see from Fig. 3, the contact between the narrower segment of chain and sprocket tooth chamfer s increases distortion value by B ⁄ 2 + s.In the next investigation, deflection position c 1 was chosen to be I, that is, c 1 = 100 mm.Then variable parameter was the changing chain distance p(y).

Tensile force of the chain
Weight force of chain depends on the sum of masses of individual chain components and equals   The structure of conveyor consists of horizontal and inclined parts.Therefore, the members in Eq. ( 6) may be separately written as Using Eq. ( 7), Eq. ( 6) looks like this Changing complex multiplier of Eq. (9.Tensile force of chain when its strand contacts with the conveyor border   where In Eq. ( 10), coefficient f s changes according to operational conditions.Therefore, two different values of mentioned coefficient were used regarding the dry and wet cases f sd and f sw , respectively.

Inclined chain part
Tensile force of chain when its strand hasn't a contact with the conveyor border: Tensile force of chain when its strand contacts with the conveyor border In explicit form Eq. ( 15) looks like this (13.1) The complex multiplier is changed by Φ, then Tensile force of chain when its strand has a contact with the conveyor border where

Inclined chain part
Tensile force of chain when the chain strand hasn't a contact with the conveyor border Tensile force of chain when its strand has a contact with the conveyor border where .In the reference [3], the rolling friction coefficient is calculated as follows In this work the following codes of modeled loading scenario of conveyor were used: NLnon-loaded; NL/0non-loaded, distorted; NL/0.35non-loaded, distorted, dry friction; L10/0.35...L50/0.35loadedby 10...50%, distorted, dry friction; Eexperimental value.

Experimental method
A distortion of chain strands was used in computation method procedure and compared with the experimental results organized using similar loading scenario and principal scheme shown in Fig. 3. Voltage and current waveforms were measured using USB data acquisition module Data Translation DT9816 with voltage transformer and current probe LEM PR200.Data acquisition module offers A/D resolution of 16 bits and simultaneous sampling of all six analogue input signals at up to 150 kHz per channel.These tools allow achieving less than 0.1% voltage and less than 1% current readout accuracy [6].
Active power consumed by the motor are RMS values of voltage and current; U m , I m are amplitudes of voltage and electric current, respectively, and  is the phase angle between the voltage and current.
The actuator force of transporter is evaluated by the following equation where η is the coefficient of efficiency of mechanical actuator; ν is the linear chain velocity.Obtained differences in the measured electric characteristics are shown in Fig. 4.

I(t)
A/D Fig. 3 Principal scheme on determination of electric power  19) and were compared with analyticaly obtained results by Eq. (20) for the same loading scenario (Fig. 6).

Exclusion of incidental load
In Fig. 5, the fragment of single chain strand is presented.
In the case of straigth chain ( If chain segment wears on the tooth with the angle 0   , transversal loading of a chain segment occures and transversal force F s starts to act.The product of this force F s and chain segment pitch p generates bending moment M(F s ) that bends a segment plate and axle, Eq. ( 22).The active loads are following: two longitudinal tensile forces   For presented computational scheme (Fig. 5), the method of superposed loads was applied.Regarding presented boundary conditions and chosen method, the loads F t and M were applied separetely.It allows us to simplify structure of equation and decrease number of members in it.Using longitudinal tensile force F t the moment balance equations give results of reactive forces R AY (F t ) and R BY (F t ) Other load, bending couple M(F s ) and moment balance equations give other two reactive forces Here, the arrows  and  mean reaction direc- tions "upsters" and "downsters", respectivelly.
To be sure that reaction forces were calculated correctly the following balance equation of forces is used Accordingly, excluded incidental loads F s and M can be used in calculations of stresses.

Stresses on the axle
Bending moment M(F s ) was replaced on the axle axis z around which the moment equation  z was written (Fig. 9).The objective was to calculate resultant shear force F sa acting on the axle Such loading conditions mentioned above were compared with Mises yield criterion for stresses [7].As it could be seen, according to presented load scenario, stress state also may represent following principal stresses In the case of principal stress, applying simplified von Mises yield criterion at axle point K , we get In explicit form, the average of normal stress in bearing could be written as    27) and Eq.(28)

Conclusions
The primary factors that led chain to start to come into contact with the conveyor frame could be asymmetrical distribution of conveyed fuel in the transport plane or the tilt of runners.Chain distortion happens yielding bad fuel and hitting the scraper.Drive shaft axis may have an inclination in relation to the horizontal plane and frontally.
Chain durability depends mostly on angle  .It increases further if scraper was dent previously and distance between the chains decreased.One of both chains during the same period of time will be much weaker than another.During operation chain distortion is the emergence of shear force F s (  ) that causes bending moment M(F s ) and bearing in the chain axle head and plate exuviations from it, too.External force F sa acting on the narrower chain segment with scraper step distance p = 80 mm is about 10 times greater than remote segment with the scraper step distance p = 640 mm.Stress 1  on the axle head of the chain is basically crucial and it comes close to ultimate stress u (Figs.11 and 12).

Fig. 1
Fig. 1 Principal kinematic scheme and used geometrical parameters

For
single chain strand chain distortion angle  evaluates scrapper length change B ⁄ 2, if scrapper goes to the sprocket teeth with chain pitch p(y) Chain distortion angle  increases if the narrower chain segment slides on the chamfer width of sprocket tooth s (Fig. 2)

Fig. 2
Fig. 2 Chain distortion angle  s versus scrapper deflection depth y max influenced by c 1 and p(y) From Eq. (1) obtained some decrease in conveyor section width B 1 gives us difference B = B 1 -B where one half of it equal B ⁄ 2. At investigated chain distance p(y) position 1 (scrapper is close to the sprocket teeth), Chain loading by its own weight and weight of conweyed material2.3.1.Horizontal chain partTensile force of chain when its strand hasn't a contact with the conveyor border inner surface of roller and external surface of axle worn down[1], then wood shavings fall between them, and at 100 % contamination by wood chips ( the similar value of coefficient of sliding friction between two metallic surfaces in dry operational conditions -35 .0  sd f

Fig. 5 
Fig. 5 Chain strand fragment and computational scheme showing balance of forces for chain members affected by resulting incidental loads F s () and M(F s ) in the case of angle 0  

-Fig. 9
Fig. 9 Axle areas showing an existance of normal stresses in bearing ( avg ) and in bending ( b ) caused by resultant shear force F sa and bending couple M(F s ), respectively: 1area of bearing; 2cross-sectional area of bending

.
Other stress members were used with the re- Axle moment influences on normal stress  b caused by bending.Such stress is expressed as follows 27)-(30) presents results shown in Fig.11.

Fig. 11
Fig. 11 Normal stresses on the axle versus chain distance   y p influenced by scrapper deflection depth

Fig. 12 1  and 2 
Fig. 12 Comparative analysis of stresses related with mechanical properties of axle material and analytically obtained values of stresses 1  and