資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 Biosystems Engineering (2006) 95(1), 3541doi:10.1016/j.biosystemseng.2006.06.007PMPower and MachineryAssessment of the Behaviour of Potatoes in a Cup-belt PlanterH. Buitenwerf1,2; W.B. Hoogmoed1; P. Lerink3; J. Mu ller1,41Farm Technology Group, Wageningen University, P.O Box. 17, 6700 AA Wageningen, The Netherlands;e-mail of corresponding author: willem.hoogmoedwur.nl2Krone GmbH, Heinrich-Krone Strasse 10, 48480 Spelle, Germany3IB-Lerink, Laan van Moerkerken 85, 3271AJ Mijnsheerenland, The Netherlands4Institute of Agricultural Engineering, University of Hohenheim, D-70593 Stuttgart, Germany(Received 27 May 2005; accepted in revised form 20 June 2006; published online 2 August 2006)The functioning of most potato planters is based on transport and placement of the seed potatoes by a cup-belt. The capacity of this process is rather low when planting accuracy has to stay at acceptable levels. Themain limitations are set by the speed of the cup-belt and the number and positioning of the cups. It washypothesised that the inaccuracy in planting distance, that is the deviation from uniform planting distances,mainly is created by the construction of the cup-belt planter.To determine the origin of the deviations in uniformity of placement of the potatoes a theoretical model wasbuilt. The model calculates the time interval between each successive potato touching the ground. Referring tothe results of the model, two hypotheses were posed, one with respect to the effect of belt speed, and one withrespect to the influence of potato shape. A planter unit was installed in a laboratory to test these twohypotheses. A high-speed camera was used to measure the time interval between each successive potato justbefore they reach the soil surface and to visualise the behaviour of the potato.The results showed that: (a) the higher the speed of the cup-belt, the more uniform is the deposition of thepotatoes; and (b) a more regular potato shape did not result in a higher planting accuracy.Major improvements can be achieved by reducing the opening time at the bottom of the duct and byimproving the design of the cups and its position relative to the duct. This will allow more room for changes inthe cup-belt speeds while keeping a high planting accuracy.r 2006 IAgrE. All rights reservedPublished by Elsevier Ltd1. IntroductionThe cup-belt planter (Fig. 1) is the most commonlyused machine to plant potatoes. The seed potatoes aretransferred from a hopper to the conveyor belt with cupssized to hold one tuber. This belt moves upwards to liftthe potatoes out of the hopper and turns over the uppersheave. At this point, the potatoes fall on the back of thenext cup and are confined in a sheet-metal duct. Atthe bottom, the belt turns over the roller, creating theopening for dropping the potato into a furrow in thesoil.Capacity and accuracy of plant spacing are the mainparameters of machine performance. High accuracy ofplant spacing results in high yield and a uniform sortingof the tubers at harvest (McPhee et al., 1996; Pavek &Thornton, 2003). Field measurements (unpublisheddata) of planting distance in The Netherlands revealeda coefficient of variation (CV) of around 20%. Earlierstudies in Canada and the USA showed even higher CVsof up to 69% (Misener, 1982; Entz & LaCroix, 1983;Sieczka et al., 1986), indicating that the accuracy is lowcompared to precision planters for beet or maize.Travelling speed and accuracy of planting show aninverse correlation. Therefore, the present cup-beltplanters are equipped with two parallel rows of cupsper belt instead of one. Doubling the cup row allowsdouble the travel speed without increasing the belt speedand thus, a higher capacity at the same accuracy isexpected.ARTICLE IN PRESS1537-5110/$32.0035r 2006 IAgrE. All rights reservedPublished by Elsevier LtdThe objective of this study was to investigate thereasons for the low accuracy of cup-belt planters and touse this knowledge to derive recommendations fordesign modifications, e.g. in belt speeds or shape andnumber of cups.For better understanding, a model was developed,describing the potato movement from the moment thepotato enters the duct up to the moment it touches theground. Thus, the behaviour of the potato at the bottomof the soil furrow was not taken into account. Asphysical properties strongly influence the efficiency ofagricultural equipment (Kutzbach, 1989), the shape ofthe potatoes was also considered in the model.Two null hypotheses were formulated: (1) the plantingaccuracy is not related to the speed of the cup-belt; and(2) the planting accuracy is not related to the dimensions(expressed by a shape factor) of the potatoes. Thehypotheses were tested both theoretically with the modeland empirically in the laboratory.2. Materials and methods2.1. Plant materialSeed potatoes of the cultivars (cv.) Sante, Arinda andMarfona have been used for testing the cup-belt planter,because they show different shape characteristics. Theshape of the potato tuber is an important characteristicfor handling and transporting. Many shape features,usually combined with size measurements, can bedistinguished (Du & Sun, 2004; Tao et al., 1995; Zo dler,1969). In the Netherlands grading of potatoes is mostlydone by using the square mesh size (Koning de et al.,1994), which is determined only by the width and height(largest and least breadth) of the potato. For thetransport processes inside the planter, the length of thepotato is a decisive factor as well.A shape factor S based on all three dimensions wasintroduced:S 100l2wh(1)where l is the length, w the width and h the height of thepotato in mm, with howol. As a reference, alsospherical golf balls (with about the same density aspotatoes), representing a shape factor S of 100 wereused. Shape characteristics of the potatoes used in thisstudy are given in Table 1.2.2. Mathematical model of the processA mathematical model was built to predict plantingaccuracy and planting capacity of the cup-belt planter.The model took into consideration radius and speed ofthe roller, the dimensions and spacing of the cups, theirpositioning with respect to the duct wall and the heightof the planter above the soil surface (Fig. 2). It wasassumed that the potatoes did not move relative to thecup or rotate during their downward movement.The field speed and cup-belt speed can be set toachieve the aimed plant spacing. The frequency fpotofpotatoes leaving the duct at the bottom is calculated asfpotvcxc(2)where vcis the cup-belt speed in ms?1and xcis thedistance in m between the cups on the belt. The angularspeed of the roller orin rad s?1with radius rrin m iscalculated asorvcrr(3)ARTICLE IN PRESS56789104321Fig. 1. Working components of the cup-belt planter: (1)potatoes in hopper; (2) cup-belt; (3) cup; (4) upper sheave;(5) duct; (6) potato on back of cup; (7) furrower; (8) roller;(9) release opening; (10) ground levelTable 1Shape characteristics of potato cultivars and golf balls used inthe experimentsCultivarSquare mesh size, mmShape factorSante2835146Arinda3545362Marfona3545168Golf balls42?8100H. BUITENWERF ET AL.36The gap in the duct has to be large enough for a potatoto pass and be released. This gap xreleasein m is reachedat a certain angle areleasein rad of a cup passing theroller. This release angle arelease(Fig. 2) is calculated ascos areleaserc xclear? xreleaserc(4)where: rcis the sum in m of the radius of the roller, thethickness of the belt and the length of the cup; and xclearis the clearance in m between the tip of the cup and thewall of the duct.When the parameters of the potatoes are known, theangle required for releasing a potato can be calculated.Apart from its shape and size, the position of the potatoon the back of the cup is determinative. Therefore, themodel distinguishes two positions: (a) minimum re-quired gap, equal to the height of a potato; and (b)maximum required gap equal to the length of a potato.The time treleasein s needed to form a release angle aois calculated astreleaseareleaseor(5)Calculating treleasefor different potatoes and possiblepositions on the cup yields the deviation from theaverage time interval between consecutive potatoes.Combined with the duration of the free fall and the fieldspeed of the planter, this gives the planting accuracy.When the potato is released, it falls towards the soilsurface. As each potato is released on a unique angularposition, it also has a unique height above the soilsurface at that moment (Fig. 2). A small potato will bereleased earlier and thus at a higher point than a largeone.The model calculates the velocity of the potato justbefore it hits the soil surface uendin ms?1. The initialvertical velocity of the potato u0in m s?1is assumed toequal the vertical component of the track speed of thetip of the cup:v0 rcorcosarelease(6)The release height yreleasein m is calculated asyrelease yr? rcsinarelease(7)where yrin m is the distance between the centre of theroller (line A in Fig. 2) and the soil surface.The time of free fall tfallin s is calculated withyrelease vendtfall 0?5gt2fall(8)where g is the gravitational acceleration (9?8ms?2) andthe final velocity vendis calculated asvend v0 2gyrelease(9)with v0in ms?1being the vertical downward speed ofthe potato at the moment of release.The time for the potato to move from Line A to therelease point treleasehas to be added to tfall.The model calculates the time interval between twoconsecutive potatoes that may be positioned in differentways on the cups. The largest deviations in intervals willoccur when a potato positioned lengthwise is followedby one positioned heightwise, and vice versa.2.3. The laboratory arrangementA standard planter unit (Miedema Hassia SL 4(6)was modified by replacing part of the bottom end of thesheet metal duct with similarly shaped transparentacrylic material (Fig. 3). The cup-belt was driven viathe roller (8 in Fig. 1), by a variable speed electric motor.The speed was measured with an infrared revolutionmeter. Only one row of cups was observed in thisarrangement.A high-speed video camera (SpeedCam Pro, Wein-berger AG, Dietikon, Switzerland) was used to visualisethe behaviour of the potatoes in the transparent ductand to measure the time interval between consecutivepotatoes. A sheet with a coordinate system was placedbehind the opening of the duct, the X axis representingthe ground level. Time was registered when the midpointof a potato passed the ground line. Standard deviationARTICLE IN PRESSxclearrc?release?xreleaseLine ALine CFig. 2. Process simulated by model, simulation starting when thecup crosses line A; release time represents time needed to createan opening sufficiently large for a potato to pass; model alsocalculates time between release of the potato and the moment itreaches the soil surface (free fall); rc, sum of the radius of theroller, thickness of the belt and length of the cup; xclear,clearance between cup and duct wall; xrelease, release clearance;arelease, release angle ; o, angular speed of roller; line C, groundlevel, end of simulationASSESSMENT OF THE BEHAVIOUR OF POTATOES37of the time interval between consecutive potatoes wasused as measure for plant spacing accuracy.For the measurements the camera system was set to arecording rate of 1000 frames per second. With anaverage free fall velocity of 2?5ms?1, the potato movesapprox. 2?5mm between two frames, sufficiently smallto allow an accurate placement registration.The feeding rates for the test of the effect of the speedof the belt were set at 300, 400 and 500 potatoes min?1(fpot 5, 6?7 and 8?3s?1) corresponding to belt speedsof 0?33, 0?45 and 0?56ms?1. These speeds would betypical for belts with 3, 2 and 1 rows of cups,respectively. A fixed feeding rate of 400 potatoes min?1(cup-belt speed of 0?45ms?1) was used to assess theeffect of the potato shape.For the assessment of a normal distribution of thetime intervals, 30 potatoes in five repetitions were used.In the other tests, 20 potatoes in three repetitions wereused.2.4. Statistical analysisThe hypotheses were tested using the Fisher test, asanalysis showed that populations were normally dis-tributed. The one-sided upper tail Fisher test was usedand a was set to 5% representing the probability of atype 1 error, where a true null hypothesis is incorrectlyrejected. The confidence interval is equal to (100?a)%.3. Results and discussion3.1. Cup-belt speed3.1.1. Empirical resultsThe measured time intervals between consecutivepotatoes touching ground showed a normal distribution.Standard deviations s for feeding rates 300, 400 and 500potatoes min?1were 33?0, 20?5 and 12?7ms, respectively.ARTICLE IN PRESSFig. 3. Laboratory test-rig; lower rightpart of the bottom end of the sheet metal duct was replaced with transparent acrylic sheet;upper rightsegment faced by the high-speed cameraH. BUITENWERF ET AL.38According to the F-test the differences between feedingrates were significant. The normal distributions for allthree feeding rates are shown in Fig. 4. The accuracy ofthe planter is increasing with the cup-belt speed, withCVs of 8?6%, 7?1% and 5?5%, respectively.3.1.2. Results predicted by the modelFigure 5 shows the effect of the belt speed on the timeneeded to create a certain opening. A linear relationshipwas found between cup-belt speed and the accuracy ofthe deposition of the potatoes expressed as deviationfrom the time interval. The shorter the time needed forcreating the opening, the smaller the deviations. Resultsof these calculations are given in Table 2.The speed of the cup turning away from the duct wallis important. Instead of a higher belt speed, an increaseof the cups circumferential speed can be achieved bydecreasing the radius of the roller. The radius of theroller used in the test is 0?055m, typical for theseplanters. It was calculated what the radius of the rollerhad to be for lower belt speeds, in order to reach thesame circumferential speed of the tip of the cup as foundfor the highest belt speed. This resulted in a radius of0?025m for 300 potatoes min?1and of 0?041m for 400potatoes min?1. Compared to this outcome, a lineartrend line based on the results of the laboratorymeasurements predicts a maximum performance at aradius of around 0?020m.The mathematical model Eqn (5) predicted a linearrelationship between the radius of the roller (forr40?01m) and the accuracy of the deposition of thepotatoes. The model was used to estimate standarddeviations for different radii at a feeding rate of 300potatoes min?1. The results are given in Fig. 6, showingthat the model predicts a more gradual decrease inaccuracy in comparison with the measured data. Aradius of 0?025m, which is probably the smallest radiustechnically possible, should have given a decrease inARTICLE IN PRESS0.0350.030f (x)0.0250.0200.0150.0100.0050.000180260500340Time x, ms420500 pot min1400 pot min1300 pot min1Fig. 4. Normal distribution of the time interval (x, in ms) ofdeposition of the potatoes (pot) for three feeding rates806448Size of opening, mm321600.000.050.100.15Time, s0.200.250.36 m s10.72 m s10.24 m s1Fig. 5. Effect of belt speed on time needed to create openingTable 2Time intervals between consecutive potatoes calculated by themodel (cv. Marfona)Belt speed,m s?1Difference between shortest and longestinterval, s0?7217?60?3629?40?2442?835302520Standard deviation, ms1510500.000.020.04Radius lower roller, m0.060.08y = 262.21 x 15.497R2 = 0.9987y = 922.1 x 17.597R2 = 0.9995Fig. 6. Relationship between the radius of the roller and thestandard deviation of the time interval of deposition of thepotatoes; the relationship is linear for radii r40?01 m, K,measurement data; m, data from mathematical model; ,extended for ro0?01 m; , linear relationship; R2, coefficient ofdeterminationASSESSMENT OF THE BEHAVIOUR OF POTATOES39standard deviation of about 75% compared to theoriginal radius.3.2. Dimension and shape of the potatoesThe results of the laboratory tests are given in Table 3.It shows the standard deviations of the time interval at afixed feeding rate of 400 potatoes min?1. These resultswere contrary to the expectations that higher standarddeviations would be found with increasing shape factors.Especially the poor results of the balls were amazing.The standard deviation of the balls was about 50%higher than the oblong potatoes of cv. Arinda. Thenormal distribution of the time intervals is shown inFig. 7. Significant differences were found between theballs and the potatoes. No significant differences werefound between the two potato varieties.The poor performance of the balls was caused by thefact that these balls could be positioned in many wayson the back of the cup. Thus, different positions of theballs in adjacent cups resulted in a lower accuracy ofdeposition. The three-dimensional drawing of the cup-belt shows the shape of the gap between cup andduct illustrating that different opening sizes are possible(Fig. 8).Arinda tubers were deposited with a higher accuracythan Marfona tubers. Analysis of the recorded framesand the potatoes, demonstrated that the potatoes of cv.Arinda always were positioned with their longest axisparallel to the back of the cup. Thus, apart from theshape factor, a higher ratio width/height will cause agreater deviation. For cv. Arinda, this ratio was 1?09, forcv. Marfona it was 1?15.3.3. Model versus laboratory test-rigThe mathematical model predicted the performanceof the process under different circumstances. The modelsimulated a better performance for spherical ballscompared to potatoes whereas the laboratory testshowed the opposite. An additional laboratory testwas done to check the reliability of the model.In the model, the time interval between two potatoesis calculated. Starting point is the moment the potatocrosses line A and end point is the crossing of line C(Fig. 2). In the laboratory test-rig the time-intervalbetween potatoes moving from line A to C wasmeasured (Fig. 3). The length, width and height of eachpotato was measured and potatoes were numbered.During the measurement it was determined how eachpotato was positioned on the cup. This position and thepotato dimensions were used as input for the model. Themeasurements were done at a feeding rate of 400potatoes min?1with potatoes of cv. Arinda andMarfona. The standard deviations of the measured timeintervals are shown in Table 4. They were slightlydifferent (higher) from the standard deviations calcu-ARTICLE IN PRESS0.0500.0450.0400.0350.0300.0250.020f (x)0.0150.0100.000245255265275285Time x, ms2953053153253350.005Marfonashape factor 168Arindashape factor 362Golf ball (sphere)shape factor 100Fig. 7. Normal distribution of the time interval (x, in ms) ofdeposition of the potatoes for different shape factors at a fixedfeeding rateFig. 8. View from below to the cup at an angle of 45 degrees;position of the potato on the back of the cup is decisive for itsreleaseTable 3Effect of cultivars on the accuracy of plant spacing; CV,coefficient of variationCultivarStandard deviation, msCV, %Arinda8?603?0Marfona9?923?5Golf balls13?244?6H. BUITENWERF ET AL.40lated by the model. Explanations for these differencesare: (1) the model does not take into considerationsituations as shown in Fig. 8, (2) the passing moment atline A and C was disputable. Oblong potatoes such ascv. Arinda may fall with the tip or with the longest sizedown. This may cause up to 6 ms difference for thepotato to reach the bottom line C.4. ConclusionsThe mathematical model simulating the movement ofthe potatoes at the time of their release from the cup-beltwas a very useful tool leading to the hypotheses to betested and to design the laboratory test-rig.Both the model and the laboratory test showed thatthe higher the speed of the belt, the more uniform thedeposition of the potatoes at zero horizontal velocity.This was due to the fact that the opening, allowing thepotato to drop, is created quicker. This leaves less effectof shape of the potato and the positioning of the potatoon