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马铃薯去皮机的设计
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山西农业大学学士学位论文（设计）文献综述 马铃薯播种机具的现状与发展摘要：综述了国内外播种机的发展现状，并通过对国内外几种典型播种机的各种参数进行系统的对比并加以分析，从中发现国产播种机与国外播种机的差距，并在此基础上去阐述我国播种机在研发和应用上所存在问题并展望未来播种机的发展趋势，同时明确马铃薯播种机的设计方向。关键词：播种机具 马铃薯 精量播种机 排种器 1. 马铃薯在我国的生产现状 马铃薯是一种高蛋白农作物，在我国得到大面积的栽种，尽管我国年产量早已跃居世界第一，然而和世界除非洲以外的其他国家和地区比起来，单产量却很低，因此在提高单产的措施上除了提高机械化生产水平外，还应该改进马铃薯的种子质量以及种植方式。 1.1我国马铃薯的生产现状300多年前，原产自美洲的马铃薯被引进中国并且逐渐成为仅次于小麦、水稻和玉米的第四大粮食作物。目前，我国的马铃薯无论是种植面积还是总产量都处于全球领先地位。从中国马铃薯网上获得的资讯：2007年我国马铃薯种植面积约8000万亩，预计总产量将超过6800万吨，占世界总产量的22%左右。单从总产量来说我国已经是世界第一，但是单产量却远远低于欧美、澳洲的水平。例如，2003年，我国马铃薯的单产量是每公顷14842公斤，低于世界平均水平的每公顷16448 公斤，还不到单产量最大的国家新西兰的每公顷44248 公斤的三分之一。1.2国外马铃薯的生产水平单产量排名前六位的国家：新西兰、比利时、丹麦、美国、英国、荷兰等欧美发达国家，他们的单产量都超过了每公顷40000 公斤（中国马铃薯网，2007）。除了地域、气候方面外，更重要的是栽培技术以及机械化生产水平的影响。显然，这些国家的农业生产机械化水平都远远高过我国。反观我国，大部分地区的马铃薯生产都还停留在人工或者半机械化生产的水平上，因此单产量低也就不足为奇。1.3目前急需解决的措施以及会遇到的困难要想提高单产量，首要的就是提高机械化生产水平。我国地域广阔，拥有多种地型，因此不可能同时提高生产机械化，所以应该根据不同的地形，不同的气候和种植方式，从而设计符合当地的农业生产机械，尽量推广播种机在农业生产中的应用。其次应该改进种植方式，我国的马铃薯种植方式一直停留在传统种植的水平上，这是急需改变的。先进的种植方式应该从改进种子质量，改进播种方式等方面进行，同时在此基础上设计相应的机械也就显得至关重要。2. 国内外播种机发展及应用的现状2.1我国播种机发展现状现目前，我国大约有500家播种机生产企业，但是这些企业中能够生产与大中型拖拉机配套的播种机的企业只有西安农业机械厂、石家庄市农业机械厂等区区10多家，其余的企业生产的都是与小型拖拉机和畜力配套的拖拉机。这种与小型拖拉机和畜力配套的播种机机的产量占全国播种机总产量的90%以上（国委文，2007）。由此可以看出当前我国已实现机械化播种的大部分地区的播种机仍以小型播种机进行传统的谷物条播为主，大中型播种机的发展远远跟不上农业生产的需要，而且大中型生产机械（包括播种机）的研制和生产水平也远远落后于发达国家的水平。2.2国外播种机发展现状相对我国而言，国外许多发达国家在第二次世界大战前后，先后完成了由传统农业向现代农业的过度和转化，经过几十年的发展，其农业机械化水平已经相当完善，现在正朝着大型化、智能化、精量化以及多功能联合型方向发展（陶卫民，2001）。美国，德国，英国等西方发达国家的发展水平已经走在世界的前列。在国外许多发达国家，精密播种机经过几十年的发展和应用，其技术水平应经达到了相当完善的程度，无论是工作速度、生产效率、工作性能、播种质量以及播种机具的通用性和适应性上都做得比较好。这对减少播种过程中的漏种率、种子损伤率和提高单产量都有很大的促进作用。现在一些发达国家正把不断更新播种机的工作原理、尽量完善其结构、延长机具使用寿命、降低制造价格和维护费用的同时提高其工作效率以及提高播种机的通用性和适应性作为未来更先进的播种机研制的发展方向。2.3与国外播种机相比，我国播种机存在的不足 和国外如美国、德国、英国等发达国家的播种机比起来，我国的播种机工作效率低，工作幅宽小，通用性和适应性低，使用可靠性不高，生产率也远较国外的低。另外，由于我国工业起步晚，因此在新技术的研制和在播种机上的应用上依旧落后于国外发达国家。下面以我国几种典型的播种机和国外的播种机作一个对比，以便从中发现我国播种机和国外先进播种机的不足。 首先，从工作效率方面来看，我国播种机的工作速度低。国外播种机的工作速度大都要求达到15h，有的甚至达到20h，受到土地，气候和一些其它因素的影响，工作速度大多采用812h，而我国工作速度大约为47h，一般工作速度为56h。比如德国早期生产的GL34T和GL36T两种机型的工作速度为7.5h(韩文锋等，2006），而我国普遍采用的2BM-2以及2BMF-2型都达不到德国这两种机型的水平。 其次，我国播种机的工作幅宽小。和国外发达国家比起来这个环节显得非常薄弱。例如西欧一些国家的生产的播种机的工作幅宽一般为56m，美国，加拿大等国家的现用机型大多可以达到1015m（陈兴田，1999）。而我国所使用的播种机的工作幅宽绝大多数低于3.5m，例如较先进的2BF-24A谷物条播机的工作幅宽为3.6m，其余的大都低于这个水平，工作幅宽低这个瓶颈在很大程度上限制了播种机的工作效率。 再次，排种器的排种效率低。我国很多使用播种机的地区在农业生产中依旧使用传统的排种方式即“一器一行”，一个排种器只能播一行种子，显然这样的效率是非常低的，即使有较先进的“一器多行”的排种器，但是技术上也表现得不够成熟，也没能进行大规模的推广及应用。国外发达国家在这方面的技术和经验就比我国先进得多，而且许多新技术已经得到广泛的应用，许多核心部件尤其是排种器无论是结构还是工作原理都还有很多值得我国学习和借鉴的地方。 最后，我国的播种机的通用性和适应性和国外发达国家比起来也还有很大的差距。在通用性方面，国外发展得比较早，技术也比较成熟，一套设备只需经过简单的更换即可实现不同种子的播种，而我国大部分播种机还都是“一机一种”，一种播种机只能够播撒一种种子，这样既浪费制造材料，又没能使播种机得到充分利用。另外，我国地域辽阔，不同的土壤条件和气候条件严重限制了播种机的适应性，在保证适应性方面的技术还很落后，而且我国研制生产的播种机很少考虑到适应性这一方面的影响。3. 我国播种机的发展趋势 虽然可以通过引进国外先进的播种机可以暂时弥补我国播种机的不足之处，但是从长远出发，我国必须走自主研发的道路，通过不断吸收国外先进技术的同时再结合我国的国情走出一条自主创新的路子，研制出具有我国特色的先进播种机。3.1加大大中型播种机的研制和开发 要想尽快缩小我国马铃薯等农作物的单产与国外水平的差距，大中型播种机将起到至关重要的作用。我国的几大平原地势平坦，比较适合大中型播种机的推广和应用。大中型播种机械除了可以节约人力，提高工作效率外还能减少种子的损伤率和漏种率，而且大中型播种机都是朝着联合作业和直接播种技术的方向发展，这种机械的优点在于：一次可以完成多项作业，作业效率高；保证及时播种，提高产量；节约能源，降低成本。3.2采用新的排种原理和排种装置 排种装置是播种机最关键的部件，先进的排种器和排种原理对播种机的效率的提高有着很重要的作用，迄今为止，我国学者几乎涉猎了世界上所有的排种器：如外槽轮式排种器、离心式排种器、各种圆盘式排种器等，而具有我国独创特色的窝眼轮式排种器、纹盘式排种器、锥盘式精量排种器也获得了广泛的应用，但是在马铃薯播种机上，先进的排种器和排种方式依然制约播种机效率的一个瓶颈。因此在已经解决种子和播种方式的情况下研制相应的播种机显得是关重要。显然，在排种器方面，我国应该朝着气流输送式条播排种器、孔带式精密排种器、气力式精密排种器以及倾斜圆盘指夹式排种器的方向发展。新的排种原理包括气力式排种原理和机械式排种原理也应得到广泛的采用（陈兴田，1999）。4. 小结一个比较先进的播种机主要取决于其几个关键的部件，如：开沟器、仿形机构、覆土器以及排种器。尤其是排种器在整个播种机结构中显得尤为重要，排种器的好坏直接关系到播种机的播种效率，因此，现在国内外播种机研制的重点依旧是放在排种器的研制上。我国在这方面也有不少的研究，尤其在气吸式排种器，窝眼式排种器还有气力式排种器的研究上有了一定的突破，但是和国外先进水平还有一定的差距，因此，我国还必须加大研制的力度。新型马铃薯已经研制成功并将实现大力推广，在将来的几年内，相应的马铃薯播种机将对这种新型马铃薯的推广起到极大的推动作用。新型的马铃薯将彻底改变传统的马铃薯块茎式播种方式，其播种方式将和玉米，油菜籽等颗粒的播种方式更为相似，但还是存在很多不同的地方，因此不能直接选用像玉米播种机或者油菜籽播种机这些现成的播种机型。由于现目前新型马铃薯还没有开始实现大面积推广，相应的马铃薯播种机具还是一片空白。基于此，对现有的马铃薯播种机和其余各类颗粒式播种机进行改进优化并在此基础上设计一种适合新型马铃薯的机械式或者气吸式播种机就成了当前以及未来相当一段时间内播种机的研制方向，同时研制的重点也将放在马铃薯播种机的排种器的研制上。参考文献：1 李宝筏农业机械学北京：中国农业出版社， 20032 朱秉兰简明农机手册郑州：河南科学技术出版社，20013 张波屏编译播种机械设计原理北京：机械工业出版社，19824 冯小静精少量播种机械使用与维修郑州：河南科学技术出版社，19985 马大敏王俊民，王秀新型农机具使用与维修北京：高等教育出版社，19966 程兴田播种机械的现状及发展前景农机与食品机械，1999，6：127 陶卫民国外农业装备发展趋势新农村，2001，7：258 刘林生英国农业机械化与农业现代化湖南农机，1999，2：259 姜宗昌2BMF2型马铃薯研制成功农业机械化与电气化，2000，5：3410 鲁滨，薛理，闰洪山等2BS5型马铃薯播种机的研制，2004，6：3311 几种马铃薯播种、种植机械 ，200712 聂延辉 江涛夹持式马铃薯播种机的探讨，2007，2：4113 周桂霞，张国庆 ，张义峰等2CM一2型马铃薯播种机的设计黑龙江八一农垦大学报，2004，16（3）：535614 赵满全，赵有杰，窦卫国等2BM9型免耕播种机关键部件的设计与研究中国农机化，2006，6：15 韩文锋，王淑红徐长征GL3 4T3 6 T型马铃薯播种机简介，2007， 1：4116 冯小静，刘俊峰，杨欣等排种器排种均匀性分析与研究河北农业大学学报，2003， 1：1416 17 赵满全，窦卫国，赵士杰，等2BSL一2型马铃薯起垄播种机的研制内蒙古农业学学报，2001， (3)：l02l0418 闰建英，樊文宪，冯占怀马铃薯施肥播种机的实验研究农机科技推广，2004，4：3419 王广胜，王玉忠，樊文宪2BXSMIB型马铃薯施肥播种机的研究农机与食品机械 ，1999，(3)：l51720 国委文播种机的现状及发展趋势。农业机械化与电气化，2007，5：3421 KACHMAN S DActernative Measures of Accuracy in Plant Spacing for Planters Using Single Seed MeteringTranslation of the ASAE，1995,38(2),pp.37137522 EUOdigbohandCOAkubuo A tworow automatic cassava cuttings planter：Development、Design and Prototype constructionJournal of Agricultural Engineering Research，Volume 50，SeptemberDecember50(1991),pp.1318 23 Tao et al., 1995 Y. Tao, C.T. Morrow, P.H. Heinemann and H.J.S. Ill, Fourier based separation technique for shape grading of potatoes using machine vision, Transactions of the ASAE 38 (1995), pp. 949957. 24 H Buitenwerf，WBHoogmoed，PLerink and JMller Assessment of the Behavior of Potato in a Cupbelt PlanterBiosystems Eigineering，95 (2006),354125Siecska et al., 1986 J.B. Sieczka, E.E. Ewing and E.D. Markwardt, Potato planter performance and effects on non-uniform spacing, American Potato Journal 63 (1986), pp. 25374Biosystems 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, s6 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 the cup. A relationship with the belt speed wasfound. So, to provide more room fo
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