畢業(yè)設(shè)計翻譯馬鈴薯性能評估

1、<p><b>　　外文資料翻譯譯文</b></p><p>　　馬鈴薯播種機(jī)的性能評估</p><p>　　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為偏離了統(tǒng)一的種植距離，這主要原因是升運鏈?zhǔn)?/p>

2、馬鈴薯播種機(jī)的構(gòu)造造成的.</p><p>　　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)。為了驗證這兩種假設(shè)，特地在實驗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動方式。</p><p&

3、gt;　　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。</p><p>　　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。</p><p><b>　?。苯榻B說明</b></p><p>　　升

4、運鏈?zhǔn)今R鈴薯種植機(jī)（圖一）是當(dāng)前運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。這條鏈向上運動使得種薯離開種子箱到達(dá)上鏈輪，在這一點上，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).</p><p>　　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。 </p><p>　　圖一，杯帶式播種機(jī)的主要工作部件：（1）種子箱；（2）輸送鏈；

5、（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。</p><p>　　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(McPhee et al, 1996；Pavek & Thornton, 2003)。在荷蘭的實地測量株距（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

6、于玉米和甜菜的精密播種，當(dāng)變異系數(shù)高達(dá)69%(Misener, 1982；Entz & LaCroix, 1983；Sieczka et al, 1986)時，其播種就精度特別低。</p><p>　　輸送速度和播種精度顯示出一種逆相關(guān)關(guān)系，因此，目前使用的升運鏈?zhǔn)椒N植機(jī)的每條輸送帶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

7、行的。</p><p>　　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。</p><p>　　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)的運動過程，因此馬鈴薯在地溝的運動情況就不在考慮之列。由于物理因素對農(nóng)業(yè)設(shè)備的強烈影響(Kutzbach, 1989)，通常要將馬鈴

8、薯的形狀考慮進(jìn)模型中。</p><p>　　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驗室論證的測試。</p><p><b>　?。膊牧霞胺椒?lt;/b></p><p><b>　　播種材料</b></p><

9、;p>　　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鏈?zhǔn)讲シN機(jī)測試，因為它們</p><p>　　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(Du & Sun, 2004； Tao et al, 1995； Zödler, 1969)。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

10、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。</p><p>　　形狀因子S的計算基于已經(jīng)提到的三種尺寸：</p><p>　　此處l是長度，w是寬度，h是高度（單位：mm），且h<w<l。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</p><p>　　

11、表一 實驗中馬鈴薯及高爾夫球的形狀特征</p><p>　　2.2 建立數(shù)學(xué)模型</p><p>　　數(shù)學(xué)模型的建立是為了預(yù)測升運鏈?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。</p><p>　　圖二，模型模

12、擬過程，當(dāng)取薯杯到達(dá)A點的時候模擬開始。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；αrelease ，釋放角度；ω, 鏈輪的角速度；C點，地溝。</p><p>　　田間作業(yè)速度和輸送帶速度可

13、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：</p><p>　　式中：vc 是勺型輸送帶的速度（單位：m s?1），xc 是帶上兩個取薯勺之間的距離（單位：m）.槽輪的角速度ωr（單位：rad s?1）計算如下：</p><p>　　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αreleas

14、e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：</p><p>　　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。</p><p>　　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

15、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。</p><p>　　釋放角度αo所需的時間trelease的計算公式如下：</p><p>　　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。</p><p>　　該

16、模型計算出馬鈴薯剛好落到地溝時的速度υend（單位：m s?1）。假定垂直方向的初速度等于取薯勺線速度的垂直分量：</p><p>　　釋放高度的計算公式為：</p><p>　　yrelease=yr-rcsinαrelease</p><p>　　yr（單位：m）是鏈輪中心和地溝的距離</p><p>　　自由下落時間的計算公式

17、為：</p><p>　　g（9.8 m s?2）是自由落體加速度，v0（單位: m)是馬鈴薯釋放時垂直下落的初速度。終止速度的計算公式為：</p><p>　　馬鈴薯從A點移動到釋放點的時間trelease還應(yīng)該加上tfall。該模型計算出以不同的方式在取薯勺上定位的兩個連續(xù)馬鈴薯之間的時間間隔。最大的誤差區(qū)間將出現(xiàn)在馬鈴薯由縱向定位趨向軸向定位的過程中，反之亦然。</p

18、><p><b>　　實驗室裝置</b></p><p>　　一個標(biāo)準(zhǔn)的播種機(jī)可以替換片狀導(dǎo)種管底部的類似透明丙烯酸的材料（圖三）。輸送鏈通過鏈輪被變速電動機(jī)驅(qū)動，其速度可以通過一個旋轉(zhuǎn)的紅外檢測儀測得。此裝置只能觀察一排取薯勺。</p><p>　　實驗室實驗臺：片狀導(dǎo)種管底端的右下部被透明的丙烯酸金屬片替代；右上端正對一個高速攝像機(jī)。</

19、p><p>　　這個攝像機(jī)通過透明的導(dǎo)種管對種薯的運動進(jìn)行攝像記錄，并測量兩個連續(xù)馬鈴薯之間的時間間隔。一張坐標(biāo)圖被安放在導(dǎo)種管的開口處，X軸平行于地面。當(dāng)種薯的中點通過地面的時候時間就被記錄下來了。連續(xù)種薯之間的時間間隔的標(biāo)準(zhǔn)偏差被用來衡量作物間距的精度。</p><p>　　為了便于測量，測量系統(tǒng)的記錄速率設(shè)置為1000幀每秒。平均自由下落的速度是2.5 m s?1時，種薯每幀的

20、移動距離是2.5 mm，足夠小到可以記錄準(zhǔn)確的位置。</p><p>　　為了測試鏈速的影響，進(jìn)料速度被分別設(shè)置為300、400、500個種薯每分鐘。（fpot =5,6.7和8.3 s?1），對應(yīng)的鏈速為0.33,0.45,0.56（m s?1）。這些速度分別對應(yīng)的是3、2、1排取薯杯。每分鐘400個種薯的進(jìn)料率（0.45 m s?1的杯帶速度）作為一個固定速度來對馬鈴薯形狀的影響進(jìn)行測評。

21、</p><p>　　為了評估時間間隔的正態(tài)分布，30個種薯將被重復(fù)使用5次。在另一個測試中20個種薯將被重復(fù)使用3次。</p><p><b>　　2.4. 統(tǒng)計分析</b></p><p>　　對上述假設(shè)進(jìn)行了Fisher測試，分析表明：總體呈正態(tài)分布。尾部進(jìn)行單因素上限分析的Fisher測試被用來檢驗頻率a為5%第一類誤差，然而一個正確的

22、零假設(shè)被錯誤地拒絕了。其置信區(qū)間等于(100?a)%</p><p><b>　　3 結(jié)果與討論</b></p><p><b>　　3.1 輸送帶速度</b></p><p>　　3.1.1 實證結(jié)果</p><p>　　測得的連續(xù)種薯觸地的時間間隔呈正態(tài)分布。進(jìn)料速度為300、400、500的標(biāo)

23、準(zhǔn)偏差</p><p>　　σ分別為33.0、20.5、12.7 ms。通過F檢驗可知進(jìn)料率的差異顯著。三種進(jìn)料率的正態(tài)</p><p>　　分布如圖四所示。當(dāng)變異系數(shù)分別為8.6%、7.1%和5.5%的時候，杯帶的速度越大則播種機(jī)的精度越高。</p><p>　　圖四.三種馬鈴薯進(jìn)料速率時間間隔的正態(tài)分布圖</p><p>　　3.1.2

24、結(jié)果模型預(yù)測</p><p>　　圖五顯示了開口形成時間對升運鏈速度的影響。鏈條的速度與沉積時偏離了時間間隔的種薯的準(zhǔn)確性呈線性關(guān)系。形成開口的時間越短，偏差越小。計算結(jié)果見表二：</p><p><b>　　圖五</b></p><p>　　表二 模型計算出來的連續(xù)種薯之間的時間間隔</p><p>　　升運鏈脫離導(dǎo)

25、種管壁的速度是很重要的一個因素。相對提高輸送帶速來說，取薯勺線速度可以通過降低鏈輪的半徑來增大。實驗中使用的鏈輪半徑是0.055米,是播種機(jī)的一般標(biāo)準(zhǔn)。為了使取薯勺的線速度達(dá)到最高的升運鏈速度，鏈輪半徑必須通過最低的鏈條速度計算。由此得出種薯進(jìn)料率為每分鐘300個和400個的半徑分別為0.025米和0.041米。與此相比，實驗室測量的結(jié)果是一條呈線性變化的直線，最大的半徑約為0.020米</p><p>　　數(shù)學(xué)

26、模型預(yù)測的結(jié)果呈一種線性關(guān)系。鏈輪的半徑和種薯沉積的精確度呈線性關(guān)系。該模型用來估計進(jìn)料率為每分鐘300個種薯的標(biāo)準(zhǔn)差。其結(jié)果如圖六所示，該模型的預(yù)測值與實測數(shù)據(jù)相比，其精度逐漸減小。顯然0.025米可能是技術(shù)上可行的最小半徑，相對于原來的半徑的標(biāo)準(zhǔn)差為75%。</p><p><b>　　圖六</b></p><p>　　圖六顯示了鏈輪半徑與沉積的種薯時間間隔標(biāo)準(zhǔn)差

27、之間的關(guān)系。當(dāng)滿足r>0·01m</p><p>　　時，這種關(guān)系是線性的?！?，測量數(shù)據(jù)；，數(shù)學(xué)模型的數(shù)據(jù)； ■，延長到R < 0 ? 01米； -，線性關(guān)系；R2，決定系數(shù)。</p><p>　　3.2 馬鈴薯的尺寸和形狀</p><p>　　實驗數(shù)據(jù)由表三給出。顯示固定進(jìn)料率為每分鐘400個種薯的時間間隔的標(biāo)準(zhǔn)偏差。這</p>

28、<p>　　些結(jié)果與期望值剛好相反，即高的標(biāo)準(zhǔn)偏差將使得形狀因子增加。球狀馬鈴薯的結(jié)果尤其令人吃驚：球的標(biāo)準(zhǔn)偏差高過阿玲達(dá)馬鈴薯50%以上。時間間隔的正態(tài)分布如圖七所示，球和馬鈴薯之間的差異明顯。兩個不同品種的馬鈴薯之間的差異不明顯。</p><p>　　表三 馬鈴薯品種對種植間距的精確度的影響</p><p>　　圖七，固定進(jìn)料率下不同形狀的沉積的馬鈴薯時間間隔的正態(tài)分布

29、</p><p>　　球狀馬鈴薯的這種結(jié)果是因為球可以以不同的方式在取薯勺背部定位。臨近杯中球的不同定位導(dǎo)致沉積精度降低。杯帶的三維視圖顯示了取薯勺與導(dǎo)種管之間的間隔的形狀，顯然獲得不同大小的開放空間是可行的。</p><p>　　圖八，取薯勺呈45度時的效果圖；馬鈴薯在護(hù)種壁的位置對其釋放具有決定性影響。</p><p>　　阿玲達(dá)塊莖種薯在沉積時比麻佛來的精度高

30、。通過對記錄的幀和馬鈴薯的分析，結(jié)果表明：阿玲達(dá)這種馬鈴薯總是被定位平行于最長的軸線的護(hù)種壁。因此，除了形狀因子外，寬度與高度的高比例值也將造成更大的偏差。阿玲達(dá)的這個比例是1.09，麻佛來的為1.15。</p><p>　　3.3 實驗室對抗模型測試平臺</p><p>　　該數(shù)學(xué)模型預(yù)測了不同情況下的流程性能。相對于馬鈴薯，該模型對球模擬了更好的性能，然而實驗測試的結(jié)果卻恰然相反。另外

31、實驗室試驗是為了檢查模型的可靠性。</p><p>　　在該模型里，兩個馬鈴薯之間的時間間隔被計算出來。起始點出現(xiàn)在馬鈴薯開始經(jīng)過A點的時刻，終點出現(xiàn)在馬鈴薯到達(dá)C點的時刻。通過實驗平臺，從A到C點的馬鈴薯的時間間隔被測出。每個馬鈴薯的長度、寬度和高度也通過測量獲得，同時記錄了馬鈴薯的數(shù)量。測量過程中馬鈴薯在取薯杯上的位置是已經(jīng)確定好的。這個位置和馬鈴薯的尺寸將作為模型的輸入量，測量過程將阿玲達(dá)與麻佛來以400個

32、馬鈴薯每分的速率下進(jìn)行。測量時間間隔的標(biāo)準(zhǔn)偏差如表四所示。測量的標(biāo)準(zhǔn)誤差與模型的標(biāo)準(zhǔn)誤差只是稍稍不同。對這種不同現(xiàn)象的解釋是：（1）模型并沒有把圖八中出現(xiàn)的情況考慮進(jìn)去；（2）從A點到C點的時間不一致。塊狀馬鈴薯如阿玲達(dá)可能從頂部或者最遠(yuǎn)距離下落，這將導(dǎo)致種薯到達(dá)C點底部的時間增加6ms</p><p>　　表四 通過實驗室測量和模型計算出來的開放時間的標(biāo)準(zhǔn)誤差的差異</p><p>&

33、lt;b>　　4. 總結(jié)</b></p><p>　　這個模擬馬鈴薯從輸送帶開始釋放的運動的數(shù)學(xué)模型是一個非常有用的證實假設(shè)和設(shè)計實驗平臺的工具。</p><p>　　模型和實驗室的測試都表明：鏈速越高，馬鈴薯在零速度水平沉積得更均勻。這是由于開口足夠大使得馬鈴薯下降得越快，這對馬鈴薯的形狀和種薯在取薯杯上的定位有一定的影響，與鏈條速度的關(guān)系也就隨之明確，因此，在保持高的

34、播種精度時，應(yīng)該提供更多的空間以減小鏈條的速度。建議降低鏈輪的半徑，直至低到技術(shù)上的可行度。</p><p>　　該研究顯示，播種機(jī)的取薯勺升運鏈鏈對播種精度（播種的幅寬）有很大的影響。</p><p>　　更規(guī)格的形狀（形狀因子低）并不能自動提高播種精度。小球（高爾夫球）在很多情況下沉積的精度低于馬鈴薯，這是由導(dǎo)向的導(dǎo)種管和取薯勺的形狀決定的。</p><p>　

35、　因此建議重新設(shè)計取薯勺和導(dǎo)種管的形狀，要做到這一點還應(yīng)該將小鏈輪加以考慮。</p><p><b>　　外文原文</b></p><p>　　Assessment of the Behaviour of Potatoes in a Cup-belt Planter</p><p>　　The functioning of most potat

36、o planters is based on transport and placement of the see 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 sp

37、eed of the cup-belt and the number and positioning of the cups. It was hypothesized that the inaccuracy in planting distance, that is the deviation from uniform planting distances, mainly is created by the construction

38、of the cup-belt planter. </p><p>　　To determine the origin of the deviations in uniformity of placement of the potatoes atheoretical model was built. The model calculates the time interval between each succ

39、essive 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 in?uence of potato shape. A planter unit was

40、installed in a laboratory to test these two hypotheses. A high-speed camera was used to measure the time inte</p><p>　　The results showed that: (a) the higher the speed of the cup-belt, the more uniform is t

41、hedeposition of the potatoes; and (b) a more regular potato shape did not result in a higher planting accuracy. </p><p>　　Major improvements can be achieved by reducing the opening time at the bottom of the

42、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. </p><p>　　1. Introduc

43、tion </p><p>　　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

44、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 confined in a sheet-metal duct. At the bottom, the belt tur

45、ns over the roller, creating the opening for dropping the potato into a furrow in the s</p><p>　　Capacity and accuracy of plant spacing are the main parameters of machine performance.High accuracy of plant

46、 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 co

47、efficient 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</p><p>　　Travelling speed a

48、nd 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 w

49、ithout increasing the belt speed and thus, a higher capacity at the same accuracy is expected. </p><p>　　The objective of this study was to investigate the reasons for the low accuracy of cup-belt planters a

50、nd to use this knowledge to derive recommendations for design modifications, e.g. in belt speeds or shape and number of cups. </p><p>　　For better understanding, a model was developed, describing the potato

51、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

52、in?uence the efficiency of agricultural equipment (Kutzbach, 1989), the shape of the potatoes was also considered in the model. </p><p>　　Two null hypotheses were formulated: (1) the planting accuracy is not

53、 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 empi

54、rically in the laboratory. </p><p>　　Fig 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; (

55、8) roller; (9) release opening; (10) ground level </p><p>　　2 .Materials and methods</p><p>　　2.1. Plant material </p><p>　　Seed potatoes of the cultivars (cv.) Sante, Arinda and Ma

56、rfona 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, u

57、sually 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

58、),which</p><p>　　A shape factor S based on all three dimensions was introduced: </p><p><b>　　(1)</b></p><p>　　Where/ is the length, w the width and h the height of the p

59、otato in mm, with h<w<l. 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 stu

60、dy are given in Table 1. </p><p>　　表一 實驗中馬鈴薯及高爾夫球的形狀特征</p><p>　　2.2. Mathematical model of the process </p><p>　　A mathematical model was built to predict planting accuracy and pla

61、nting 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 plan

62、ter 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. </p><p>　　The field speed and cup-belt speed can be set to ach

63、ieve the aimed plant spacing. The frequency fpot of potatoes leaving the duct at the bottom is calculated as </p><p><b>　　(2)</b></p><p>　　where v c is the cup-belt speed in m s?1and

64、 xc is in the distance in m between the cups on the belt. The angular speed of the roller ωr in rad s?1 with radius r r in m is calculated as </p><p><b>　　(3)</b></p><p>　　The gap in

65、 the duct has to b e large enough for a potato to pass and be released .This gap xrelease in m is reached at a certain angle αrelease in rad of a cup passing the roller. This release angle αrelease (Fig.2) is calculated

66、 as </p><p>　　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.

67、 </p><p>　　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 dete

68、rminative. Therefore, the model distinguishes two positions: (a) minimum required gap, equal to the height of a potato; and (b) maximum required gap equal to the length of a potato. </p><p>　　The time trelea

69、se in s needed to form a release angle a0 is calculated as </p><p>　　Calculating trelease for different potatoes and possible positions on the cup yields the deviation from the average time interval between

70、consecutive potatoes.</p><p>　　Combined with the duration of the free fall and the field speed of the planter, this gives the planting accuracy. </p><p>　　When the potato is released, it falls t

71、owards 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

72、point than a large one. </p><p>　　The model calculates the velocity of the potato just before it hits the soil surface υend in m s?1 The initial vertical velocity of the potato vo in m s is assumed to equal

73、the vertical component of the track speed of the tip of the cup: </p><p>　　The release height yrelease in m is calculated as</p><p>　　yrelease=yr-rcsinαrelease</p><p>　　Where yr in

74、m is the distance between the centre of the roller (line A in Fig.2) and the soil surface.</p><p>　　The time of free fall tfall in s is calculated with</p><p>　　where g is the gravitational acce

75、leration(9.8ms-2) and the final velocity vend is calculated as</p><p>　　with vo in ms-1 being the vertical downward speed of the potato at the moment of release.</p><p>　　The time for the potato

76、 to move from Line A to the release point trelease has to be added to t fall. </p><p>　　The model calculates the time interval between two consecutive potatoes that may be positioned in different ways on the

77、 cups. The largest deviations in intervals will occur when a potato positioned lengthwise is followed by one positioned heightwise, and vice versa.</p><p>　　Fig. 2. Process simulated by model, simulation st

78、arting when the cup crosses line A; release time represents time needed to create an opening sufficiently large for a potato to pass; model also calculates time between release of the potato and the moment it reaches the

79、 soil surface (free fall); r c, sum of the radius of the roller, thickness of the belt and length of the cup; xclear, clearance between cup and duct wall; xrelease , release clearance; xrelease release angle ;w,angular s

80、peed of ro</p><p>　　2.3. The laboratory arrangement </p><p>　　A standard planter unit (Miedema Hassia SL 4(6)) was modified by replacing part of the bottom end of the sheet metal duct with simil

81、arly 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

82、was observed in this arrangement. </p><p>　　A high-speed video camera (SpeedCam Pro, Wein- berger AG, Dietikon, Switzerland) was used to visualise the behaviour of the potatoes in the transparent duct and to

83、 measure the time interval between 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 po

84、tato passed the ground line. Standard deviation of the time interval between consecutive potatoes was used as measure</p><p>　　For the measurements the camera system was set to a recording rate of 1000 frame

85、s per second. With an average free fall velocity of 2.5 m s -1,the potato moves approx 2.5 mm between two frames, sufficiently small to allow an accurate placemen registration. </p><p>　　The feeding rates

86、for the test of the effect of the speed of the belt were set at 300, 400 and 500 potatoes min-1(fpot=5,6.7and8.3s-1) corresponding to belt speeds of 0.33,.0.45 and 0.56ms-1. These speeds would be </p><p>　　

87、Typical for belts with 3, 2 and 1 rows of cups, (cup-belt speed of 0.45 m s -1) was used to assess the effect of the potato shape. </p><p>　　For th assessment of a normal distribution of the time intervals

88、, 30 potatoes in five repetitions were used. In the other tests, 20 potatoes in three repetitions were used. </p><p>　　2.4. Statistical analysis </p><p>　　The hypotheses were tested using the Fi

89、sher test, as analysis showed that populations were normally distributed. The one-sided upper tail Fisher test was used</p><p>　　and a was set to 5% representing the probability of a type 1 error, where a tr

90、ue null hypothesis is incorrectly rejected. The confidence interval is equal to (100_a)%. </p><p>　　Fig.3. Laboratory test-rig; lower right—part of the bottom end of the sheet metal duct was replaced with t

91、ransparent acrylic sheet; upper right—segment faced by the high-speed camera</p><p>　　3. Results and discussion </p><p>　　3.1. Cup-belt speed </p><p>　　3.1.1. Empirical results <

92、;/p><p>　　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-1were 33_0, 20_5 and 12_7 m

93、s, respectively.</p><p>　　According to the F-test the differences between feeding rates were significant. The normal distributions for all three feeding rates are shown in Fig. 4. The accuracy of the planter

94、 is increasing with the cup-belt speed, with CVs of 8.6%, 7.1% and 5.5%, respectively. </p><p>　　3.1.2. Results predicted by the model </p><p>　　Figure 5 shows the effect of the belt speed on th

95、e 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 nee

96、ded for creating the opening, the smaller the deviations. Results of these calculations are given in Table 2. </p><p>　　The speed of the cup turning away from the duct wall is important Instead of a higher b

97、elt speed, an increase of the cup's circumferential speed can be achieved by decreasing the radius of the roller. The radius of the roller used in the test is 0.055 m, typical for these planters. It was calculated wh

98、at the radius of the roller.</p><p>　　Fig. 4. Normal distribution of the time interval (x, in ms) of deposition of the potatoes (pot) for three feeding rates</p><p>　　Fig.5. Effect of

99、 belt speed on time needed to create opening</p><p><b>　　Table 2 </b></p><p>　　Time intervals between consecutive potatoes calculated by the model (cv. Marfona)</p><p>　

100、　Fig6. Relationship between the radius of the roller and the standard deviation of the time interval of deposition of the potatoes; the relationship is linear for radii r>0.01 m, ● measurement data; ▲data from mathe

101、matica model; ■,extended for r<0.01 m; —, linear relationship; R2 , coefficient of determination </p><p>　　had to be for lower belt speeds, in order to reach the same circumferential speed of the tip of

102、the cup as found for the highest belt speed. This resulted in a radius of potatoes min-1 Compared to this outcome, a linear trend line based on the results of the laboratory measurements predicts a maximum performance

103、 at a radius of around 0_020 m. </p><p>　　The mathematical model[Eqn(5) predicted a linear relationship between the radius of the roller (for r>0.01m) and the accuracy of the deposition of the pot

104、atoes. 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 accurac