1-s2.0-S014294181400261X-main

Material behaviourBallistic and numerical simulation of impacting goods on conveyor belt rubberW.Molnar a,*,S.Nugent a,M.Lindroos b,M.Apostol b,M.Varga aa AC2T research GmbH,Viktor-Kaplan-Straße2C,2700Wiener Neustadt,Austriab Tampere Wear Center,Department of Materials Science,Tampere University of Technology,P.O.Box589,33101Tampere,Finlanda r t i c l e i n f oArticle history:Received27October2014 Accepted2December2014 Available online11December2014Keywords:RubberBallistic impactSimulationTribologyConveyor belt a b s t r a c tImpact loading is an important process in the transport industry as it causes wear and failure of critical components.Conveyor belts are of particular importance as they are used in practically every industry where large quantities of goods are moved over short(<10m) or long distances(>1km).To investigate stress levels inside the material during impact loading,a gas gun was utilized to shoot9mm spherical steel balls onto the surface of a rubber conveyor belt.A high speed video recording system was employed in order to determine penetration depth and dissipated energy of the steel ball.Maximal penetration depths of up to3.9mm and maximal dissipated energies of up to86.8%were measured. Additionally,a numerical simulation using smooth particle applied mechanics was con-ducted and compared to the experimental results obtained with the gas gun.The calcu-lated von Mises stresses affected the conveyor belts up to a maximum depth of8.8mm with at least20MPa.Maximum von Mises stresses were calculated to reach60MPa.©2014Elsevier Ltd.All rights reserved.1.IntroductionWear and failure of critical components are major con-cerns in every industry.Therefore,preventing or slowing down wear is one of the most important,but also most challenging,aspects of design.In this case,the loading process of rubber based conveyor belts is of particular in-terest.Depending on the application,conveyor belts can be loaded with hundreds of tons of goods every hour,which causes elastic,as well as plastic,deformation of the mate-rial and,over time,wear.The belt can make up to70%of the total costs of a transport system(calculated as cost per lifetime)[1],emphasising the importance of its wear resistance.To tackle this problem,one mustfirst understand the process of loading and impacting.One option is to run a large number of tests and experimentally simulate every possible outcome.Unfortunately,this is very time-consuming and expensive and,in most cases,impracti-cable.An elegant solution is a numerical simulation,which can quickly deliver values for set parameters once a suitable model has been chosen and corresponding code written. Such simulation can also give insight on phenomena that are not directly accessible via practical experiments,such as stress inside the material,change of contact geometry or tribo-chemical effects[2].Of course,there is still a need for experimentally acquired results to validate the chosen model.Over the years,different experimental setups have been designed to test materials for their impact related proper-ties,generating data that can be used to compare with data from numerical simulations.Wang et al.[3]used a high-speed crash system,where a trolley was accelerated by an elastic rope onto a rigid wall.A numerical simulation with a finite element model provided validation of data.Another possible setup includes a gas gun to simulate single particle impact,which was reported by Apostol et al.[4].Currently,*Corresponding author.E-mail address:molnar@ac2t.at(W.Molnar).Contents lists available at ScienceDirect Polymer Testingjou rn al homepage:/l ocate/polytest/10.1016/j.polymertesting.2014.12.0010142-9418/©2014Elsevier Ltd.All rights reserved.Polymer Testing42(2015)1e7impact simulations are used to predict impact-related wear due to erosion[5,6],blast resistance[7]and ballistics[8].In literature,numerical simulations,whether they are based on continuum,discrete or statistical methods,are often utilized in modelling tribological phenomena to enhance understanding of problems that are not accessible through experimental approaches alone[9].It is also possible to model such phenomena with a particle-based method:the smoothed particle applied mechanics (SPAM),as described recently by Sun et al.[10].This method relies on particles shifting around a defined grid according to equations of motion.The physical properties being investigated are gained through interpolation between these mass-carrying particles.Since the interpolation is a summation of the influence by neighbouring particles,theydo not carry volume elements,but parts of it,and summa-tion gives the quantity investigated.SPAM-related models have been used successfully in the past by Johnson et al.[11] to simulate pared to simulation methods like finite elements,SPAM can deal more efficiently with large deformations,which are expected when investigating rub-ber,and offer better accuracy in such situations.Depending on the kinetic energy of the impacting ball, wear and damage mechanisms can differ greatly.Thus,the model must be adjusted to the specific material pairing and kinetic energy.A visco-elastic model is needed in this case, as the objects being investigated are rubber conveyor belts.A couple of models have been used in literature to simulate visco-elastic impact[12].For modelling linear visco-elasticity,the well-established Kelvin-Voigt model and the Maxwell model can be used as a basis.This work will utilize the Kelvin-Voigt model,which includes a purely viscous dampener and a purely elastic spring.The SPAM model will contain a purely elastic material together with a viscous term,representing spring and dampener.Therefore,this work will focus on understanding the impact situation,with an emphasis on the stresses present during the loading process of rubber conveyor belts.In contrast to other works,which concentrate on homoge-nous materials to reduce the number of interpretable pa-rameters,this work tries to take the influence of the carcass into account,which more accurately reflects the practical usage of conveyor belts.2.Experimental2.1.MaterialsA basic schematic is shown in Fig.1,illustrating the complex makeup and material combination of a state of the art conveyor belt,which is composed of:A4mm thick rubber top layer and three layers of an interwoven polyester(warp)-polyamide(weft)carcass with skim layers (made of soft rubber)between them to improve the tensile strength of the belt.A2mm rubber bottom layer completes the conveyor belt and provides sufficient friction to the drive pulley during service.Two commercially available Styrene-Butadien-Rubber (SBR)based conveyor belts,Semperit Multiply D(Sample A)and Transconti NQ(Sample B),were chosen for these experiments.Additionally,Semperit N17was selected (Sample C).This particular belt is also SBR based and fea-tures additionally a deformingfleece for better processing. Shore A hardness was measured for all three samples and revealed values of65,63and71for Samples A,B,and C, respectively.Square plates,with lateral dimensions of180Â180mm and a total thickness of10mm,were sawn from of the original conveyor belts.These samples were thenfixed to a tiltable table using steel clamps.2.2.Impact testingThe impact tests at high velocity were performed using a High Velocity Particle Impactor(HVPI).A schematic drawing of the device is presented in Fig.2.The HVPI consists of a smooth bore barrel connected to a pressurised air tank so that9mm balls of various materials can be launched onto prepared samples.To monitor the velocity at impact,a speed measurement device was placed just before the target assembly.The target assembly is angled at 45 and consists of the samplesfixed onto a steel support with clamps.The impact was monitored by a high speed camera and evaluated for subsequent analysis.The HVPI device uses pressurized air to launch spherical projectiles in a controlled manner against a piece of conveyor belt placed at1m distance from the end of the barrel.A stainless steel ball of9mm in diameter and2.98g in weight was used as a projectile.The projectile balls were fired against the samples at a constant velocity of37m/s, which corresponds to a kinetic energy prior the impact of 2.04J.The incident velocity of the projectile was measured by a commercial timing device placed in front of the target assembly.The impact tests were performed at an angle of 45 with a precision of±1 .Each sample was impacted ten times to observe effects of hysteresis or damage caused by previous impacts and to ensure statistical significance.The fractions of dissipated energy of the initial kinetic energies,maximum penetration depths and reflected an-gles were determined by analysing several overlapping high speed images.Fig.3illustrates the overlapping tech-nique,where the yellow dash-dot line defines the impact surface(zero line)and the blue circles highlight the surface of the impacting steel ball.To calculate the exit velocity,the distance travelled(D s) between frames after the impact event was calculated by tracking a specific point,such as the centroid of theball.Fig.1.Schematic cross-section of a state of the art conveyor belt.W.Molnar et al./Polymer Testing42(2015)1e7 2The exit velocity is then used to calculate the dissipated energy (E d )fractions.E d ¼m p Àv 2i Àv 2eÁ2;(1)where m p ,v i ,v e ,represent the mass of the particle,themeasured incident velocity and the calculated exit velocity of the particle,respectively.The maximum penetration depths (D p )were also quanti fied via image analysis by determining the maximum de flection of the rubber surface with respect to the original surface (zero line)during the impact event.In addition,the projectile velocity and deceleration were calculated as functions of time by using all captured high speed images in order to analyze changes in material properties throughout the experiment.2.3.Simulation e SPAMThe simulations were done with the scheme of Smoothed Particle Applied Mechanics close to theformulation of Nugent et al.[14].Any continuum or field function f(r,v)at a location r with a velocity v is represented as a weighted sum of the contributions from the neigh-bouring particles [15]:〈f ðr ;v Þ〉¼mX N j ¼11r ðr j Þf ðr j ;v j Þw ðj r Àr j j ;h Þ(2)So,N particles each carry the same mass m and con-tinuum values,such as density r j .If one applies the gradient to this function,it only applies to r ,so only the gradient of the kernel has to be considered.The kernel.w ij ¼w ðj r i Àr j j ;h Þ(3)is usually an even function with a finite carrier of radius h ,called the smoothing length.We use the Lucy kernel in this work [14,16],which vanishes smoothly at radius r !h .For simulation of solids,the equations have to be modi fied regarding the representation of the stress-strain relation s -ε[17].With the density being integrated from the continuity relation,the SPAM equations of motion (equations (4)e (8))become:d r ðr i Þ¼m X N j ¼1ðv i Àv j ÞV i w ij(4)dr idt¼v i (5)d v i dt ¼m X N j ¼1s i i þs ij !$V i w ij þF v þF e(6)d εi dt¼Àm 2X Nj ¼11ffiffiffiffir i p r j ÀÀv i Àv j Á5V w ij þð…Þt Á(7)d s i dt ¼l tr d εi dtþ2m d εidt(8)For the force due to viscosity F v ,we use the arti ficial viscosity described by Monaghan [15],with a beingaFig.2.Schematic of the high velocity particle impactor (HVPI)[13].Fig.3.Five stages of the impact event recorded with a high speed cameraduring HVPI testing,showing the analysed values [13].W.Molnar et al./Polymer Testing 42(2015)1e 73viscous parameter and h ¼a r hc/20being the viscosity,where c is the velocity of sound.F e represents external forces,for instance boundary forces.Boundary conditions are modelled by mirror particles [18],ideal plasticity by multiplying the stress with a reduction factor,which compares the yield with the von Mises stress [17],and tangential plasticity with a tangential adjustment of the yield.The whole simulated area equals an isotropic plate with dimensions of 28Â28Â10mm (LxWxH)with an incompressible layer placed on the bottom (the opposite side from the impact).3.Results3.1.Experimental impact simulationThe penetration depth and dissipated energy acquired during the experiments with the HVPI gas gun can be observed in Fig.4.As expected,the majority of the steel ball's kinetic energy was dissipated by the impact on the conveyor belt surface (Fig.4a,b).From the original kinetic energy of 2J,the ball lost between 86.1%(Sample A)and 86.8%(Samples B and C).All three samples show practically the same amount of dissi-pated energy (which is why only a very narrow range is shown in Fig.4b)and also feature very similar evolution of dissipated energy during impact.It can,therefore,be concluded that the dissipated energy shows no relation to Shore A hardness,which is different for the samples.The penetration depths (Fig.4c,d)reached a maximum of 3.9mm for Sample A,3.6mm for Sample B and 3.1mm for Sample C.It is also not surprising that the deforming fleece in Sample C causes the lowest penetration depth,as the textile fibres distribute the force of the impact more ef ficiently and stiffen the rubber because of the fibres'higher elastic modulus.It is widely accepted that there are no universal equa-tions for calculating a rubber's visco-elastic properties from its mechanical properties,and mathematical models only apply for a very limited set of parameters [19].Further-more,at such high penetration depths,the carcass and skim layers are starting to interact with the impacting steel ball.Hence,it is not surprising that the penetration depths do not correlate with the Shore A hardness of the rubber covers,which is used more for its historical importance than its applicability [20].Another interesting detail is that the dissipation of the energy takes roughly 0.25ms,while it takes 0.45ms for the penetration depth to revert to 0mm.It seems that the energy is only dissipated in considerable amounts when certain penetration depths are reached.The steel ball loses most of its speed in an interval of 0.15ms,so only within three data-points.It can be concluded that the recording speed of 20.000fps (one frame every 0.05ms)was probably too low to investigate certain details of the impact.However,the image quality (reduced resolution)deteriorated at higher recording speeds and reduced the accuracy of the optical analysis.Ten impacts were performed per sample and used to calculate the standard deviations in Figs.4b,d.RubbermayFig.4.Dissipated energy during HVPI testing as functions of time (a)and as maximum values (b)for Samples A,B and C.Analogously,penetration depths functions of time (c)and maximum penetration depths (d)for the three samples are shown.W.Molnar et al./Polymer Testing 42(2015)1e 74show a hysteresis depending on its loading process history [19],but no signs of hysteresis were observed at HVPI testing.Also,no signs of wear were observed in the impact zone after the investigation.The standard deviations overlap for the maximum dissipated energy,therefore their absolute values can be considered equal,although the maximum penetration depths show clear differences.Consequently,the results from Fig.4show very similar results for all three samples regarding dissipated energy.Samples A and B are again similar,as their standard de-viations overlap.Sample C,on the other hand,clearly exhibits a lower value than the other two.This is probably due to the deforming fleece worked into the top layer of Sample C.3.2.Numerical impact simulationAll of the experimentally acquired values were used as a foundation for a numerical simulation using SPAM.Fig.5shows the results of the SPAM simulation as described above.As exact values are unknonwn,the simulations were conducted in the form of a parameter variation study,where the E-modulus and the viscosity parameter a were varied to determine the curves closest to the experimental values.Calculations were made for E-moduli of 0.01,0.05and 0.1GPa,as rubber can be expected to exhibit values in this region.Also,values of 0.3,0.5and 0.7were taken for the viscosity parameter a ,which is the standard range for elastomers.An E-modulus of 0.01GPa and a ¼0.3in the SPAM simulation produced yield results that best fit the experi-mental curves and,therefore,best describe the behaviourof the investigated rubber conveyor belts.The penetration depth (Fig.5a)reached maximum values of 3mm,which is in good agreement with the experimental values varying from 3.1mm to 3.4mm.The calculated time for the dura-tion of impact,on the other hand,does not fit the experi-mental values so well:0.45and 0.50ms were measured during the experiments,while calculated values reach 0.7ms.The evolution of the ball's dissipated energy (Fig.5b)most closely replicates the experimental results when E is set to 0.10GPa and a is set to 0.5.As before,a large differ-ence can be seen between the duration of the impact calculated numerically (0.2ms)and measured experi-mentally (0.45ms).A minimum was observed in the function of the ball's energy over time,which corresponds to the point where the steel ball had its lowest velocity.Then,the energy rises slightly,as the stored energy in the rubber is partly retransferred to the steel ball.This effect was not observable in the experiments,as the recording speed was too low to investigate such details.Clearly,the numerical simulation offers improved insight into impact behaviour.Fig.6shows the distribution of the von Mises stresses and a 3D illustration of the rubber material during different stages of the impact calculated with the SPAM simulation.The simulation of the von Mises stresses revealed that the highest concentration of stress can be expected along the impact direction of the steel ball and reaches values up to 60MPa.Although the rubber is affected by stress practically over the entire thickness during the impact,the impact region near the trailing edge is affected muchless.Fig.5.Penetration depth (a)and dissipated energy of the ball (b)calculated by adjusting the E-modulus (E)and the viscosity parameter (a )in SPAM simulations.W.Molnar et al./Polymer Testing 42(2015)1e 754.DiscussionContrary to the simulation with a sliding ball on rubber conducted by Fukahori et al.[21],there was no second high stress concentration at the trailing edge.This shows that these two kinds of motion cannot be compared directly,as the stress distribution takes a different form.Consequently,impact on rubber cannot be investigated correctly by sliding experiments or simulations.Other,more impact-related,works in literature concentrate on military appli-cations,such as the propagation of shockwaves and dam-age caused by bullets (Leavy et al.[8]),involving too much kinetic energy to be considered realistic for impacts on conveyor belt transport systems.Further interesting in-vestigations were conducted by Cenna et al.[22],who used a similar gas gun to study the impact on ductile materials.Due to the ductility,the deformation remained intact,allowing greater insight into the development of the deformation and how the material was affected.Cenna et al.also observed two zones.The first zone,situated in the impact direction of a spherical particle,featured high stress and deformation.The second zone represented the defor-mation of the bulk and was shaped more symmetrically around the impact.The numerical simulation conducted in this work con firmed the observations made by Cenna et al.,as the same stress distribution was calculated.Fig.7shows the affected depth,which is de fined here as the depth of the sample affected by stresses of 20MPa or more,and the depth where the highest stress concentra-tion was found (depth of highest stress).The dotted line illustrates the thickness of the top layer,i .e .the part of the rubber that is intended to absorb the impact.The values were calculated from the simulation depicted in Fig.6.At 0.07ms,the early state of impact with only 1.6mm penetration depth,the affected depth already reaches 4.7mm and in fluences the carcass.At its maximum,the affected depth reaches a value of 8.8mm e far beyond the thickness of the 4mm top layer and,theoretically,already reaching into the bottom layer beyond the carcass.The depths of highest stress,on the other hand,do not exceed 4mm and remain concentrated slightly above the carcass.Therefore,the carcass already crucially in fluences the impact behaviour of rubber conveyor belts at relatively low energy levels.As the calculations were conducted without taking a carcass into consideration,the simulated impact behaviour does not match with that observed during ex-periments perfectly.Nonetheless,useful insight into sur-face wear and destruction-related phenomena was gained by this investigation:Affected depths already exceed the top layer thickness by far at 2.04J impact.For high-impact environments,thick top layers should be considered in order to guarantee long life cycles of conveyor belts.The next step for understanding the complex conveyor belt structure and tailoring wear resistant solutions should involve consideration of the carcass as well,despite its complex model,dif ficult reproduction and increased de-mand in computing capability.5.ConclusionsThe results from the ballistic experiments with a gas gun served as a basis for the SPAM-based numerical simulation.The kinetic energy of the steel ball and the penetration depth was recorded throughout the test and then compared to the simulated values.While fitting the kinetic energies and penetration depths was done satis-factorily,the calculated time until impact was always about 25%shorter than in the experiments.Also,different pa-rameters for E and a were necessary to ensure the best fit for each quantity.Therefore,it can be deduced that the chosen model lacks some details.It would be necessary to apply a more complex model that takes into account the in fluence and behaviour of the carcass and skim layers,as the penetration depths are high enough to make consid-ering the in fluence of these parts necessary.Nonetheless,the stress distribution was calculated satisfactorily.The maximum affected depth during the impacts reaches 8.8mm,proving that not only the top layer is affected,but also the carcass.Hence,thick top layers are worth consid-ering for application,depending on kinetic energy and size of the impacting particles.AcknowledgmentsThis work was funded by the “Austrian Comet-Pro-gram ”(governmental funding program forpre-competitiveFig.6.Von Mises stress distribution and 3D illustration of the rubber ma-terial during different stages of the impact with parameter:E ¼0.01GPa and a ¼0.3.Fig.7.Affected stress and the depth of the highest stress concentration calculated from the numerical simulation.Parameters:E ¼0.01GPa;a ¼0.3.W.Molnar et al./Polymer Testing 42(2015)1e 76research;Project XTribology,no.824187)via the Austrian Research Promotion Agency(FFG)and was carried out at the“Austrian Center of Competence for Tribology”(AC2T research GmbH)and at Tampere Wear Center,Department of Materials Science,Tampere University of Technology. 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