The Simulation of the Impact Damage to Fruit During the Passage of a Truck Over a Speed Bump by Means of the Discrete Element Method

Research Paper: PHdPostharvest Technology The simulation of the impact damage to fruit during the passage of a truck over a speed bump by means of the discrete element method Michael Van Zeebroeck a, *, Geert Lombaert b,1 , Edward Dintwa a , Herman Ramon a , Geert Degrande b , Engelbert Tijskens a a Department of Biosystems, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium b Department of Civil Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 40,
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  Research Paper: PH d Postharvest Technology The simulation of the impact damage to fruit during thepassage of a truck over a speed bump by means of the discrete element method Michael Van Zeebroeck a, *, Geert Lombaert b,1 , Edward Dintwa a , Herman Ramon a ,Geert Degrande b , Engelbert Tijskens a a Department of Biosystems, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium b Department of Civil Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 40, B-3001 Leuven, Belgium a r t i c l e i n f o Article history: Received 11 December 2007Received in revised form 10 March2008Accepted 2 June 2008The discrete element method (DEM) was used to study fruit damage during transportation.The DEM is a particle-based simulation technique which is well suited for the solution of granular material related problems in food and agriculture. In this paper, the applicationof DEM to food transport problems was demonstrated by simulation of bruising to applesstored in bulk bins during the passage of a truck over a speed bump. The effects of truckload, bulk bin position, suspension type and driving speed on damage were investigated.The simulations showed that higher truck loads lead to less bruising and that apples inbulk bins behind the rear axle suffered more damage than those in bulk bins in front of the rear axle. Furthermore, a considerable reduction in the damage was predicted in sim-ulations where the truck has a soft suspension. Independent of truck load, suspension typeand bulk bin position, the commercially significant bruising (i.e. apples with bruise volumeof maximum bruise above 500 mm 3 ) was predicted to be insignificant for driving speeds be-low 20 kmh  1 . At higher driving speeds, the extent of commercially acceptable bruising de-pended on various parameters. A reduction in the driving speed, an increase in the truckload and a reduction in the suspension stiffness all helped to reduce the occurrence of fruitdamage. ª  2008 IAgrE. Published by Elsevier Ltd. All rights reserved. 1. Introduction For most fruits bruising is the most common type of posthar-vest mechanical injury. Fruit bruising does not only affect thequality appreciated by the consumer, but bruises open thepathways for pathogenic attack, even when they are smallin size. The present study deals with bruising caused by tran-sient vibrations or shocks. This form of damage is more fre-quently encountered than damage due to static compression(Mohsenin, 1973).Intheliterature,onlyalimitednumberofstudiesdealwiththe effect of transient vibrations on fruit impact damage. Holt *  Corresponding author . Flemish Ministry of Agriculture and Fishery, Ellipsgebouw – Koning Albert II, Laan 35, Bus 40, B-1030 Brussel,Belgium.E-mail address: (M. Van Zeebroeck). 1 Postdoctoral Fellow of the Research Foundation – Flanders (FWO). Available at www.sciencedirect.comjournal homepage: 1537-5110/$ – see front matter  ª  2008 IAgrE. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.biosystemseng.2008.06.003 biosystems engineering 101 (2008) 58–68  andSchoorl(1985)and Jones etal. (1991)developedanumericalmodel for the simulation of impact damage of apples due totransient shocks caused by road discontinuities such asbumps and potholes. Their model accounted for the interac-tion between the road, the vehicle and the load. The appleswere assumed to be stacked in vertical columns, so that thereare only two potential bruise sites on each apple. The follow-ing three sub-problems were considered: (1) modelling andcharacterisation of the road surface roughness, (2) predictionof the vertical vehicle response for a given road unevenness,(3) prediction ofthe contactinteractionof the fruit (energyab-sorption in their study, but possibly also contact forces) andcorrelation of fruit interactions with bruising. The equationsof motion of this system were solved numerically by meansof the Runge–Kutta or the Adams–Bashforth method. In thestudy by Jones  et al.  (1991), apple bruising was predicted asa function of the truck load, the bulk bin position, the bumpheight and the truck driving speed.A more accurate representation of the dynamic behaviourof the stacked apples can be obtained by means of the dis-crete element method (DEM). The DEM is a numerical tech-nique to model the kinematic and dynamic behaviour of particles. In the case of packed fruit, each particle representsa single piece of fruit. In the DEM all forces acting on the par-ticles (gravity force and contact force) are considered and theequations of motion of Newton and Euler are integrated toobtain the velocity and position of the particles in the nexttime step. The DEM was srcinally developed in the field of rock mechanics and has been used extensively for engineer-ing materials, but applications for biological materials arescarce, in particular for soft biological materials such as fruit.When used for the simulation of the dynamic behaviour of packed fruit, the rotation of the apples, the impact with allsurrounding objects and the friction between the applescan be accounted for. Pioneering work with two-dimensionalDEM simulations of in-transit fruit damage was carried outby Rong   et al.  (1993) for a total of 12 particles (i.e. apples).The contact forces between the apples were simulated fortwo types of road irregularities (curbs and ramps) and forboth soft and stiff vehicle suspensions.In order to improve the control of mechanical fruit han-dling with respect to bruising, a generic three-dimensionalDEM model was implemented in the DEMeter þþ software byTijskens etal. (2003).VanZeebroeck etal. (2006a,b)alsoappliedthis model to simulate the dynamic behaviour of packed ap-ples.Newmeasuringtechniquesthatallowforthedetermina-tion of the impact parameters of biological materials in thenormal and tangential directions have also been developed.Furthermore, the use of the DEM in the simulation of impactdamage of fruit has been validated and DEM simulationshave been applied to investigate impact damage of applesdue to continuous vibrations during transport (Tijskens et al. , 2003; Van Zeebroeck  et al. , 2003, 2004, 2006a,b; Dintwa et al. , 2004, 2005a,b).Inthispaper,three-dimensionalDEMsimulationsareusedtoinvestigateimpactdamagecausedbythepassageofatruckon a speed bump for apples in completely filled commercialbulk bins. Furthermore, the influence of truck load, positionof the bulk bin, vehicle suspension type and vehicle speedon fruit damage are investigated. 2. Materials and methods 2.1. Two-stage approach The simulation of the apple impact damage during the pas-sage of the truck over a speed bump was performed in twostages. In the first stage, a two-dimensional vehicle model of a Volvo FL6 truck was used to predict the dynamic responseof the truck during passage over the speed bump. In the sim-ulations, the static load of the bulk bins was taken into ac-count, while the dynamic interaction between the vehiclebody and the bulk bins was disregarded. This is a reasonableassumption when no loss of contact occurs between the ap-ples, the bulk bin and the vehicle body and when the reso-nance frequency of the bulk bin with the stacked apples isrelatively high compared with the resonance frequencies of the vehicle. In the second stage, the dynamic response of the vehicle body was used to excite the apples in the bulkbin. The vertical response of the truck body depends on thesuspension stiffness, position, driving speed and total truckload was investigated. A soft suspension, where the value of the suspension stiffness was halved, and a stiff suspension,wherethestiffnesswasdoubled,werealsoconsidered.Thevi-brations of the vehicle body were considered at three posi-tions: (1) at the rear axle, (2) 2 m in front of the rear axle and(3)2 m behindthe rearaxle. Thevehiclespeedvariedbetween20 kmh  1 and 50 kmh  1 . Three different loading conditionswere considered for the truck: lightly loaded, half loaded,and fully loaded.The dynamic response of the vehicle body was subse-quentlyusedtodeterminethedynamicresponseoftheapplesby means of the DEM simulations. The box (bulk bin) in thesimulations has a length of 1.15 m and a width of 0.96 m, cor-responding to the size of commercial bulk bins used in Bel-gium. The simulations were performed using DEMeter þþ ,a library of C þþ  DEM routines developed at the KatholiekeUniversiteit Leuven. Each simulation considered 1512 applesin a maximum stack height of 0.57 m. It was assumed thatthe diameter of the apples could be represented by a normaldistribution with an average value of 0.076 m and a standarddeviationof0.0076 m,coveringtheentirerangeofcommercialapple diameter classes. The influence of the aforementionedparameters on the apple bruising was investigated by meansof a total of 90 DEM simulations. In each simulation, 7 s real-time are simulated in a computation time of 40 min using a computer equipped with a P4 processor operating at a speedof 2.4GHz and a dynamic memory of 512 MB RAM. In the sim-ulation, the first 2 s were used to obtain a natural stacking of the apples in the bulk bin, which was simulated by dropping the apples from a certain height into the box. This eventwas not taken into account when determining bruising. Theremaining 5 sin thesimulationcoveredtheverticalexcitationof the box by passage over the speed bump. 2.2. Road–vehicle model In this section, the dynamic response of a truck during thepassage on a speed bump is considered. The focus was onthe response at the rear of the vehicle body, where the cargo biosystems engineering 101 (2008) 58–68  59  waspresent.Thecalculations wereperformed forthe particu-lar case of a two-axleVolvo FL6 truck. TheVolvo FL6 truck hasa wheel base of 5.20 m and a maximum total mass of 14,000 kg. Similar types of trucks are frequently used forroad transport of fruit. The simulations were performedwith Matlab (Mathworks, Natick, MA, USA).Inthefollowing,thecaseisconsideredwherea sinusoidal-shaped speed bump excites the vehicle. The longitudinal un-evenness profile  u w/r (  y ) of the speed bump represents the de-viation of a travelled surface from a true planar surface ateach position  y  along the road: u w = r ð y Þ¼ H 2  1 þ cos  2 p yL   for   L 2  y  L 2 (1)In Belgium, the Royal Decree of 9 October 1998 prescribeda height  H ¼ 0.12 m and a length  L ¼ 4.80 m for this type of speed bump (Fig. 1a) (NN, 1998). These parameters were cho- sen such that the increase of the car body accelerations, andhence the discomfort of the driver, was the strongest ata speed of 30 kmh  1 . A forward Fourier transformation withrespecttothelongitudinalcoordinate  y revealsthewavenum-ber content  ~ u w = r ð k y Þ  of the profile (Fig. 1b). The wavenumbercontentshowedzerosat k  yn ¼ 2 p n  / L ( n > 1)andwasmainlysit-uated in the range of wavenumbers  k  y  below 2.6 radm  1 orwavelengths  l  y ¼ 2 p  / k  y  longer than 2.4 m.As the speed bump excited the vehicle simultaneouslyalongbothwheelpaths,atwo-dimensionalvehiclemodelsuf-ficed. The main interest was in the calculation of the dynamicresponse in a frequency range between 0 Hz and 20 Hz. In thisfrequencyrange,thevehiclebodyandaxlesareassumedtoberigid and models for the simulation of vehicle ride behaviouras shown in Fig. 2 are used (Cebon, 1993). The vehicle body and axles are represented by discrete masses, while the sus-pension system and the tyres are modelled as a spring-dashpot system.As part of an experimental validation for the predictionmethodforgroundvibrationsduetoroadtraffic,alinearvehi-cle model was developed for the Volvo FL6 truck (Lombaertand Degrande, 2003). This is shown in Fig. 2. The parameters of the inertial elements and the spring constants have beendeterminedfromweighings, informationfromthetruckman-ufacturer and an experimental modal analysis. The damping constants have been estimated from a fit of the predictedand measured frequency content of the axle response during a passage of the truck on a ply-wood unevenness at a speed v ¼ 30 kmh  1 . The following values were used (Lombaert et al. , 2000; Lombaert and Degrande, 2003): the mass of the ve-hicle body  m b ¼ 9000 kg, the rotational inertia of the body I b ¼ 35,000 kgm 2 . The position of the rear and front axleswith respect to the centre of gravity was  l 1 ¼ 1.49 m and l 2 ¼ 3.72 m, respectively. In the following, the position of therear axle position is referred to as the position  y ¼ l 1 ; the posi-tion at 2 m in front of the rear axle is the position  y ¼ l 1 þ 2 m,while the position at 2 m behind the rear axle is the y ¼ l 1  2 m position.The mass of the rear and front axles was  m a1 ¼ 600 kg and m a2 ¼ 400 kg, respectively. The spring constants of the rearand front suspensions were  k p1 ¼ 0.61  10 6 Nm  1 and k p2 ¼ 0.32  10 6 Nm  1 . The corresponding damping constantsare  c p1 ¼ 16,000 Nsm  1 and  c p2 ¼ 10,050 Nsm  1 . The spring constants of the rear and front tyres are  k t1 ¼ 3.00  10 6 Nm  1 and k t2 ¼ 1.50  10 6 Nm  1 .Thedampingconstants ofthetyreswere assumed to be zero, so that  c t1 ¼ 0 Nsm  1 and c t2 ¼ 0 Nsm  1 . This mathematical model of the Volvo FL6truck has been shown to successfully predict the ground vi-brations during a passage of the truck over the ply-woodbump for a range of vehicle speeds between 20 kmh  1 and60 kmh  1 (Lombaert and Degrande, 2003). 2.3. Discrete element model In the DEM simulations, the parameters for the normal andtangential contact force models and the bruise prediction Fig. 1 – (a) The longitudinal road profile  u w/r (   y  ) of a sine-shaped traffic bump as a function of the coordinate  y  alongthe road and (b)  ~ u w = r ð k  y Þ  in the wavenumber domain.Fig. 2 – Two-dimensional 4DOF model for a vehicle withtwo axles. biosystems engineering 101 (2008) 58–68 60  given by Van Zeebroeck  et al.  (2003) and Van Zeebroeck  et al. (2006a) were used. These parameters are briefly summarisedhere.A pendulum device was used to develop a contact forcemodel that describes the apple-metal impact. The model con-sisted of the parallel connection of a spring and a damper. Forthe particular case of ‘‘Jonagold’’ apples, the following valuesfor the damping constants  c  (kgm  1/2 s  1 ) and the spring con-stants  k  (Nm  3/2 ) have been determined experimentally byVan Zeebroeck  et al.  (2003) (both  R 2 ¼ 0.38): c R  ¼ 914  465 v þ 8 : 7 r  (2) c G  ¼ 914  465 v þ 8 : 7 r  (3) k R  ¼ 336712  434707 v þ 38732 r  (4) k G  ¼ 1117131  434707 v þ 11664 r  (5)wherethe subscripts R and G referto the red and green side of the apple, respectively, while  v  denotes the impact velocity(ms  1 ) and  r  is the radius of curvature (mm). According tothe classical Hertz contact theory, the spring constant de-pends on the effective radius of curvature. Kuwabara andKono (1987) derived the damping constant in a similar way.Furthermore, the parameters also depended on the impactvelocity, as discussed in detail by Van Zeebroeck (2005).Although the parameters were only valid for the impact of apples on a hard wall, they could be modified to representthe contactforcesforcontactbetweenapples(Van Zeebroeck,2005). The values above indicate that the damping and spring constants were higher for the red side of the ‘‘Jonagold’’ applecomparedtothegreenside.However,intheDEMsimulations,distinctions were not made between the sides and averagevalues were used to determine the contact force. In anticipa-tion of the implementation of the viscoelastic extension of the Mindlin and Deresiewicz model in the DEMeter þþ  soft-ware (Dintwa  et al. , 2005a,b) a tangential contact force modelbased on dry Coulomb friction was applied. A value of 0.27was used for the dynamic friction coefficient in the tangentialcontact force model since it had been determined experimen-tally for apple–apple contact (Van Zeebroeck  et al. , 2004). Thesame value was also applied for the contact between the ap-ples and the wall.BasedontheDEMresultsforthecontactforces,thelevelof bruising was determined. The model of  Chen and Sun (1981)was used to predict bruise volume (BV) from the peak value(PF)ofthecontactforce.Aregressionanalysisbasedonresultsfrom the pendulum device determined the following relation-ship:BV ¼ 15 : 81PF  608 : 90 (6)with a coefficient of determination ( R 2 ) of 0.90. In the simula-tions, the location of the impact on the apple surface was notstored. This requires a local coordinate system for each parti-cle, a feature that was currently, not then available, in theDEMeter þþ software. The BV was therefore interpreted as be-ing the ‘‘single impact’’ BV. A validation of the model can befound in Van Zeebroeck  et al.  (2006a). The calculation of theBV was performed in Matlab, allowing for further analysis of the occurred damage, such as the histogram of the numberof apples with the volume of the largest bruise in a certaindamage class and the number of apples with damage abovea certain threshold. 3. Results 3.1. Road–vehicle simulation Inthe simulations, as thevehicletraversedthe speedbump,itwasexcitedbyanimposeddisplacement u w/r (  y )atthecontactpointsbetweenthevehicleandtheroad.Thisimpliedthatthevehicle was assumed to remain in perfect contact with theroad and that the flexibility of the road was disregarded.The time history of the excitation was determined by the ve-hicle speed  v  and obtained from  u w/r (  y ), replacing   y  by  vt .Fig. 3a shows the time history of the excitation at the frontaxle for vehicle speeds of 10 kmh  1 , 30 kmh  1 and50 kmh  1 . These three cases will be considered here. Apartfrom a small time delay, the rear axle experienced the sameexcitation.As the vehicle model was linear, the equations of motionwere solved in the frequency domain. The frequency content  b u w = r ð u Þ of the imposed displacement was calculated from therepresentation  ~ u w = r ð k y Þ of the unevenness in the wavenumberdomain:  b u w = r ð u Þ¼ 1 v ~ u w = r   u v   (7) Fig. 3 – (a) Time history  u w/r (  t   ) and (b) frequency content   b u w = r ð u Þ of the signal applied at the vehicle axles during thepassage on a speed hump at 10 kmh L 1 (dotted line),30 kmh L 1 (solid line) and 50 kmh L 1 (dashed line). biosystems engineering 101 (2008) 58–68  61
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