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- 1 - Assessment of the Behaviour of Potatoes in a Cup-belt Planter H. Buitenwerf; W.B. Hoogmoed; P. Lerink;J.Muller Farm Technology Group, Wageningen University, P.O Box. 17, 6700 AA Wageningen, The Netherlands; e-mail of corresponding author: willem.hoogmoedwur.nl Krone GmbH, Heinrich-Krone Strasse 10, 48480 Spelle, Germany IB-Lerink, Laan van Moerkerken 85, 3271AJ Mijnsheerenland, The Netherlands Institute 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. The main limitations are set by the speed of the cup-belt and the number and positioning of the cups. It was hypothesised 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 was built. The model calculates the time interval between each successive potato touching the ground. Referring to the results of the model, two hypotheses were posed, one with respect to the effect of belt speed, and one with respect to the inuence of potato shape. A planter unit was installed in a laboratory to test these two hypotheses. A high-speed camera was used to measure the time interval between each successive potato just before 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 the potatoes; 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 by improving the design of the cups and its position relative to the duct. This will allow more room for changes in the cup-belt speeds while keeping a high planting accuracy. 1. Introduction The cup-belt planter (Fig. 1) is the most commonly used machine to plant potatoes. The seed potatoes are transferred from a hopper to the conveyor belt with cups sized to hold one tuber. This belt moves upwards to lift the potatoes out of the hopper and turns over the upper sheave. At this point, the potatoes fall on the back of the next cup and are conned in a sheet-metal duct. At the bottom, the belt turns over the roller, creating the opening for dropping the potato into a furrow in the soil. Capacity and accuracy of plant spacing are the main parameters of machine performance. High accuracy of plant spacing results in high yield and a uniform sorting of the tubers at harvest (McPhee et al., 1996; Pavek & Thornton, 2003). Field measurements (unpublished data) of planting distance in The Netherlands revealed a coefcient of variation (CV) of around 20%. Earlier studies in Canada and the USA showed even higher CVs of up to 69% (Misener, 1982; Entz & LaCroix, 1983; Sieczka et al., 1986), indicating that the accuracy is low compared to precision planters for beet or maize. Travelling speed and accuracy of planting show an inverse correlation. Therefore, the present cup-belt planters are equipped with two parallel rows of cups per belt instead of one. Doubling the cup row allows double the travel speed without increasing the belt speed and thus, a higher capacity at the same accuracy is expected. 附 錄 - 2 - The objective of this study was to investigate the reasons for the low accuracy of cup-belt planters and to use this knowledge to derive recommendations for design modications, e.g. in belt speeds or shape and number of cups. For better understanding, a model was developed, describing the potato movement from the moment the potato enters the duct up to the moment it touches the ground. Thus, the behaviour of the potato at the bottom of the soil furrow was not taken into account. As physical properties strongly inuence the efciency of agricultural equipment (Kutzbach, 1989), the shape of the potatoes was also considered in the model. Two null hypotheses were formulated: (1) the planting accuracy 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. The hypotheses were tested both theoretically with the model and empirically in the laboratory. 2. Materials and methods 2.1. Plant material Seed potatoes of the cultivars (cv.) Sante, Arinda and Marfona have been used for testing the cup-belt planter, because they show different shape characteristics. The shape of the potato tuber is an important characteristic for handling and transporting. Many shape features, usually combined with size measurements, can be distinguished (Du & Sun, 2004; Tao et al., 1995; Zodler, 1969). In the Netherlands grading of potatoes is mostly done 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 the transport processes inside the planter, the length of the potato is a decisive factor as well. A shape factor S based on all three dimensions was introduced: where l is the length, w the width and h the height of the potato in mm, with howol. As a reference, also spherical golf balls (with about the same density as potatoes), representing a shape factor S of 100 were used. Shape characteristics of the potatoes used in this study are given in Table 1. - 3 - 2.2. Mathematical model of the process A mathematical model was built to predict planting accuracy and planting capacity of the cup-belt planter. The model took into consideration radius and speed of the roller, the dimensions and spacing of the cups, their positioning with respect to the duct wall and the height of the planter above the soil surface (Fig. 2). It was assumed that the potatoes did not move relative to the cup or rotate during their downward movement. The eld speed and cup-belt speed can be set to achieve the aimed plant spacing. The frequency fpot of potatoes leaving the duct at the bottom is calculated as where vc is the cup-belt speed in ms-1 and xc is the distance in m between the cups on the belt. The angular speed of the roller or in rad s -1 with radius rr in m is calculated as 附 錄 - 4 - This gap xrelease in m is reached at a certain angle arelease in rad of a cup passing the roller. This release angle arelease (Fig. 2) is calculated as where: rc is the sum in m of the radius of the roller, the thickness of the belt and the length of the cup; and xclear is the clearance in m between the tip of the cup and the wall of the duct. When the parameters of the potatoes are known, the angle required for releasing a potato can be calculated. Apart from its shape and size, the position of the potato on the back of the cup is determinative. Therefore, the model 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 trelease in s needed to form a release angle ao is calculated as Calculating trelease for different potatoes and possible positions on the cup yields the deviation from the average time interval between consecutive potatoes. Combined with the duration of the free fall and the eld speed of the planter, this gives the planting accuracy. When the potato is released, it falls towards the soil surface. As each potato is released on a unique angular position, it also has a unique height above the soil surface at that moment (Fig. 2). A small potato will be released earlier and thus at a higher point than a large one. The model calculates the velocity of the potato just before it hits the soil surface uend in ms-1. The initial vertical velocity of the potato v0 in ms-1 is assumed to equal the vertical component of the track speed of the tip of the cup: where yr in m is the distance between the centre of the roller (line A in Fig. 2) and the soil surface. The time of free fall tfall in s is calculated with where g is the gravitational acceleration (9.8ms2) and the nal velocity vend is calculated as with v0 in ms-1 being the vertical downward speed of the potato at the moment of release. The time for the potato to move from Line A to the release point trelease has to be added to tfall. The model calculates the time interval between two consecutive potatoes that may be positioned in different ways on the cups. The largest deviations in intervals will occur when a potato positioned lengthwise is followed by one positioned heightwise, and vice versa. 2.3. The laboratory arrangement A standard planter unit (Miedema Hassia SL 4(6) was modied by replacing part of the bottom end of the sheet metal duct with similarly shaped transparent acrylic material (Fig. 3). The cup-belt was driven via the roller (8 in Fig. 1), by a variable speed electric motor. The speed was measured with an infrared revolution meter. Only one row of cups was observed in this arrangement. A high-speed video camera (SpeedCam Pro, Wein-berger AG, Dietikon, Switzerland) was used to visualize the behaviour of the potatoes in the transparent duct and to measure the time interval between - 5 - consecutive potatoes. A sheet with a coordinate system was placed behind the opening of the duct, the X axis representing the ground level. Time was registered when the midpoint of a potato passed the ground line. Standard deviation of the time interval between consecutive potatoes was used as measure for plant spacing accuracy. For the measurements the camera system was set to a recording rate of 1000 frames per second. With an average free fall velocity of 2.5ms-1, the potato moves approx. 2.5mm between two frames, sufciently small to allow an accurate placement registration. The feeding rates for the test of the effect of the speed of the belt were set at 300, 400 and 500 potatoes min-1(fpot = 5, 6.7 and 8.3s-1) corresponding to belt speeds of 0.33, 0.45 and 0.56ms-1. These speeds would be typical for belts with 3, 2 and 1 rows of cups, respectively. A xed feeding rate of 400 potatoes min-1 (cup-belt speed of 0.45ms-1) was used to assess the effect of the potato shape. For the assessment of a normal distribution of the time intervals, 30 potatoes in ve repetitions were used. In the other tests, 20 potatoes in three repetitions were used. 2.4. Statistical analysis The hypotheses were tested using the Fisher test, as analysis showed that populations were normally dis-tributed. The one-sided upper tail Fisher test was used and a was set to 5% representing the probability of a type 1 error, where a true null hypothesis is incorrectly rejected. The condence interval is equal to (100-a)%. 附 錄 - 6 - 3. Results and discussion 3.1. Cup-belt speed The measured time intervals between consecutive potatoes touching ground showed a normal distribution. Standard deviations s for feeding rates 300, 400 and 500 potatoes min-1 were 33.0, 20.5 and 12.7ms, respectively. According to the F-test the differences between feeding rates were signicant. The normal distributions for all three feeding rates are shown in Fig. 4. The accuracy of the planter is increasing with the cup-belt speed, with CVs of 8.6%, 7.1% and 5.5%, respectively. 3.2. Results predicted by the model Figure 5 shows the effect of the belt speed on the time needed to create a certain opening. A linear relationship was found between cup-belt speed and the accuracy of the deposition of the potatoes expressed as deviation from the time interval. The shorter the time needed for creating the opening, the smaller the deviations. Results of these calculations are given in Table 2. The speed of the cup turning away from the duct wall is important. Instead of a higher belt speed, an increase of the cups circumferential speed can be achieved by decreasing the radius of the roller. The radius of the roller used in the test is 0.055m, typical for these planters. It was calculated what the radius of the roller had to be for lower belt speeds, in order to reach the same circumferential speed of the tip of the cup as found for the highest belt speed. This resulted in a radius of 0.025m for 300 potatoes min-1 and of 0.041m for 400 potatoes min-1. Compared to this outcome, a linear trend line based on the results of the laboratory measurements predicts a maximum performance at a radius of around 0.020m. The mathematical model Eqn (5) predicted a linear relationship between the radius of the roller (for r4001m) and the accuracy of the deposition of the potatoes. The model was used to estimate standard deviations for different radii at a feeding rate of 300 potatoes min-1. The results are given in Fig. 6, showing that the model predicts a more gradual decrease in accuracy in comparison with the measured data. A radius of 0.025m, which is probably the smallest radius technically possible, should have given a decrease in standard deviation of about 75% compared to the original radius. 4. Conclusions The mathematical model simulating the movement of the potatoes at the time of their release from the cup-belt was a very useful tool leading to the hypotheses to be tested and to design the laboratory test-rig. Both the model and the laboratory test showed that the higher the speed of the belt, the more uniform - 7 - the deposition of the potatoes at zero horizontal velocity. This was due to the fact that the opening, allowing the potato to drop, is created quicker. This leaves less effect of shape of the potato and the positioning of the potato on the cup. A relationship with the belt speed was found. So, to provide more room for reductions in the cup-belt speeds while keeping a high planting accuracy it is recommended to decrease the radius of the roller till as low as technically possible. This study showed that the accuracy of planting (distance in the seeding furrow) is inuenced for a large part by the cup-belt unit of the planter. A more regular shape (lower shape factor) does not automatically result in a higher accuracy. A sphere (golf ball) in most cases was deposited with a lower accuracy than a potato. This was caused by the shapes of the guiding duct and cups. It is recommended to redesign the geometry of the cups and duct, and to do this in combination with a smaller roller. 附 錄 - 8 - 馬鈴薯播種機(jī)的性能評估 原文來源: H. Buitenwerf, W.B. Hoogmoed, P. Lerink and J. Mller.Assement of the Behavior of Potato in a Cup-belt Planter. Biosytems. Engineering, Volume 95, Issue, September 2006: 35 41 大多數(shù)馬鈴薯播種機(jī)都是通過勺型輸送鏈對馬鈴薯種子進(jìn)行輸送和投放。當(dāng)種植精度 只停留在一個可接受水平的時候這個過程的容量就相當(dāng)?shù)?。主要的限制因素是:輸送帶的速度以及取薯勺的?shù)量和位置。假設(shè)出現(xiàn)種植距離的偏差是因?yàn)槠x了統(tǒng)一的種植距離,這主要原因是升運(yùn)鏈?zhǔn)今R鈴薯播種機(jī)的構(gòu)造造成的 . 一個理論的模型被建立來確定均勻安置的馬鈴薯的原始偏差,這個模型計算出兩個連續(xù)的馬鈴薯觸地的時間間隔。當(dāng)談到模型的結(jié)論時,提出了兩種假設(shè),一種假設(shè)和鏈條速度有關(guān),另一種假設(shè)和馬鈴薯的形狀有關(guān)。為了驗(yàn)證這兩種假設(shè),特地在實(shí)驗(yàn)室安裝了一個種植機(jī),同時安裝一個高速攝像機(jī)來測量兩個連續(xù)的馬鈴薯在到達(dá)土壤表層時的時間間 隔以及馬鈴薯的運(yùn)動方式。 結(jié)果顯示:( a)輸送帶的速度越大,播撒的馬鈴薯越均勻;( b)篩選后的馬鈴薯形狀并不能提高播種精度。 主要的改進(jìn)措施是減少導(dǎo)種管底部的開放時間,改進(jìn)取薯杯的設(shè)計以及其相對于導(dǎo)種管的位置。這將允許杯帶在保持較高的播種精度的同時有較大的速度變化空間。 1.介紹說明 升運(yùn)鏈?zhǔn)今R鈴薯種植機(jī)(圖一)是當(dāng)前運(yùn)用最廣泛的馬鈴薯種植機(jī)。每一個取薯勺裝一塊種薯從種子箱輸送到傳送鏈。這條鏈向上運(yùn)動使得種薯離開種子箱到達(dá)上鏈輪, 在這一點(diǎn)上, 馬鈴薯種塊 落在 下一個取薯勺的背面 ,并局限于金屬導(dǎo)種 管 內(nèi) . 在底部 ,輸送鏈通過下鏈輪獲得足夠的釋放空間使得種薯落入地溝里。 圖一:杯帶式播種機(jī)的主要工作部件:( 1)種子箱;( 2)輸送鏈;( 3)取薯勺;( 4)上鏈輪;( 5)導(dǎo)種管;( 6) 護(hù)種壁 ;( 7)開溝器;( 8)下鏈輪輪;( 9)釋放孔;( 10)地溝。 株距和播種精確度是評價機(jī)械性能的兩個主要參數(shù)。高精確度將直接導(dǎo)致高產(chǎn)以及馬鈴薯收獲時的統(tǒng)一分級。在荷蘭的實(shí)地測量株距(未發(fā)表的數(shù)據(jù))變異系數(shù)大約為 20%。美國和加拿大早期的研究顯示,相對于玉米和甜菜的精密播種,當(dāng)變異系數(shù)高達(dá) 69%時,其播種就精度特別 低。 輸送速度和播種精度顯示出一種逆相關(guān)關(guān)系,因此,目前使用的升運(yùn)鏈?zhǔn)椒N植機(jī)的每條輸送帶 - 9 - 上都裝備了兩排取薯勺而不是一排。雙排的取薯勺可以使輸送速度加倍而且不必增加輸送帶的速度。因此在相同的精度上具有更高的性能是可行的。 該研究的目的是調(diào)查造成勺型帶式種植機(jī)精度低的原因, 并利用這方面的知識提出建議,并作設(shè)計上的修改 。例如在輸送帶的速度、取薯杯的形狀和數(shù)量上。 為了便于理解,建立一個模型去描述馬鈴薯從進(jìn)入導(dǎo)種管到觸及地面這個時間段內(nèi)的運(yùn)動過程,因此馬鈴薯在地溝的運(yùn)動情況就不在考慮之列。由于物理因素對農(nóng)業(yè)設(shè)備的強(qiáng) 烈影響 (Kutzbach, 1989),通常要將馬鈴薯的形狀考慮進(jìn)模型中。 兩種零假設(shè)被提出來了:( 1)播種精度和輸送帶速度無關(guān);( 2)播種精度和篩選后的種薯形狀(尤其是尺寸)無關(guān)。這兩種假設(shè)都通過了理論模型以及實(shí)驗(yàn)室論證的測試。 2.材料及方法 2.1 播種材料 幾種馬鈴薯種子如圣特、阿玲達(dá)以及麻佛來都已被用于升運(yùn)鏈?zhǔn)讲シN機(jī)測試,因?yàn)樗鼈?有不同的形狀特征。對于種薯的處理和輸送來說,種薯塊莖的形狀無疑是一個很重要的因素。許多形狀特征在結(jié)合尺寸測量的過程中都能被區(qū)分出來。在荷蘭,馬鈴薯的等級主要是由馬鈴薯的寬度和 高度(最大寬度和最小寬度)來決定的。種薯在播種機(jī)內(nèi)部的整個輸送過程中,其長度也是一個不可忽視的因素 。 形狀因子 S 的計算基于已經(jīng)提到的三種尺寸: 此處 l 是長度, w 是寬度, h 是高度(單位: mm),且 hwl。還有球形高爾夫球(其密度和馬鈴薯密度大致相同)作為參考。同是,在研究中用到的馬鈴薯的形狀特征通過表一給出 表一 實(shí)驗(yàn)中馬鈴薯及高爾夫球的形狀特征 品種 方形網(wǎng)目尺寸,毫米 形狀因子 圣特 28 35 146 阿玲達(dá) 35 45 362 麻佛來 35 45 168 高爾夫球 42.8 100 2.2 建立數(shù)學(xué)模型 數(shù)學(xué)模型的建立是為了預(yù)測升運(yùn)鏈?zhǔn)讲シN機(jī)的播種精度和播種性能,該模型考慮了滾軸的半徑和速度,取薯勺的尺寸和間距,以及它們相對于導(dǎo)種管壁的位置和地溝的高度(如圖二)。模型假設(shè)馬鈴薯在下落的過程中并沒有相對于取薯勺移動或者相對于軸轉(zhuǎn)動。 附 錄 - 10 - 圖二,模型模擬過程,當(dāng)取薯杯到達(dá) A 點(diǎn)的時候模擬開始。釋放時間是開啟一個足夠大的空間讓土豆順利通過所需的時間。該模型同時也計算出兩個連續(xù)的馬鈴薯之間的時間間隔以及馬鈴薯到達(dá)地面(自由下落)的時間。 rc 代表鏈輪半徑、帶 的厚度以及取薯杯長度之和; xclear ,取薯勺與導(dǎo)種管壁之間的間距; xrelease 釋放的間距; release ,釋放角度; , 鏈輪的角速度; C 點(diǎn),地溝。 田間作業(yè)速度和輸送帶速度可設(shè)定為達(dá)到既定的作物間距的要求。馬鈴薯離開導(dǎo)種管底部的頻率 fpot 通過如下公式計算: 式中: vc 是勺型輸送帶的速度(單位: m s1), xc 是帶上兩個取薯勺之間的距離(單位: m) .槽輪的角速度 r(單位: rad s1)計算如下: 導(dǎo)種管的間距必須足夠大以使得馬鈴薯能通過并被釋放。 xrelease是當(dāng)取薯勺 以一定的角度 release徑向通過鏈輪時的時間間距。釋放角(圖二)按以下公式進(jìn)行計算: rc(單位: m)是鏈輪半徑,鏈條的厚度以及取薯勺長度之和; xclear(單位: m)是取薯勺端面與導(dǎo)種管管壁之間的間隙。 當(dāng)馬鈴薯的各種參數(shù)已確定的情況下,釋放馬鈴薯的所需角度可以通過計算得到。除了形狀和尺寸,護(hù)種壁的馬鈴薯的位置也具有訣定性的作用,因此,這個模型區(qū)分了兩種狀態(tài):( a) 最小需求間距等于馬鈴薯的高度;( b)最大需求間距等于馬鈴薯的高度。 釋放角度 o所需的時間 trelease的計算公式如下: 當(dāng)馬鈴 薯釋放后,將直接落到地溝。由于每個馬鈴薯都是在一個特定的角度釋放的,通常那時都有一個高于地面的高度(圖二)。由于小一點(diǎn)的馬鈴薯釋放得早,因此通常將小塊馬鈴薯放在大塊馬鈴薯的上方。 該模型計算出馬鈴薯剛好落到地溝時的速度 end(單位: m s1)。假定垂直方向的初速度等于取薯勺線速度的垂直分量: 釋放高度的計算公式為: yrelease=yr-rcsin release yr(單位: m)是鏈輪中心和地溝的距離 自由
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