馬鈴薯片干燥機的設計,馬鈴薯片干燥機的設計,馬鈴薯,土豆,干燥機,設計 Biosystems Engineering (2006) 95(1), 3541 doi:10.1016/j.biosystemseng.2006.06.007 PMPower and Machinery Strasse opening for dropping the potato into a furrow in the soil. planters are equipped with two parallel rows of cups per belt instead of one. Doubling the cup row allows ARTICLE IN PRESS parameters of machine performance. High accuracy of plant spacing results in high yield and a uniform sorting and thus, a higher capacity at the same accuracy is expected. Capacity and accuracy of plant spacing are the main double the travel speed without increasing the belt speed 1537-5110/$32.00 35 r 2006 IAgrE. All rights reserved 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 influence 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. r 2006 IAgrE. All rights reserved Published by Elsevier Ltd 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 confined in a sheet-metal duct. At the bottom, the belt turns over the roller, creating the of the tubers at harvest (McPhee et al., 1996; Pavek Entz 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 Assessment of the Behaviour of H. Buitenwerf 1,2 ; W.B. Hoogmoed 1 Farm Technology Group, Wageningen University, P.O e-mail of corresponding author: 2 Krone GmbH, Heinrich-Krone 3 IB-Lerink, Laan van Moerkerken 85, 3271AJ 4 Institute of Agricultural Engineering, University (Received 27 May 2005; accepted in revised form Potatoes in a Cup-belt Planter 1 ; P. Lerink 3 ;J.Mu ller 1,4 Box. 17, 6700 AA Wageningen, The Netherlands; willem.hoogmoedwur.nl 10, 48480 Spelle, Germany Mijnsheerenland, The Netherlands of Hohenheim, D-70593 Stuttgart, Germany 20 June 2006; published online 2 August 2006) Published by Elsevier Ltd for handling and transporting. Many shape features, usually combined with size measurements, can be distinguished (Du Tao et al., 1995; Zo dler, 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. ARTICLE IN PRESS H. BUITENWERF ET AL.36 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 modifications, e.g. in belt speeds or shape and 7 8 9 10 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; (8) roller; (9) release opening; (10) ground level 5 6 432 1 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 influence the efficiency 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 The field speed and cup-belt speed can be set to achieve the aimed plant spacing. The frequency f of pot potatoes leaving the duct at the bottom is calculated as f pot v c x c (2) where v c is the cup-belt speed in ms C01 and x c is the distance in m between the cups on the belt. The angular speed of the roller o r in rad s C01 with radius r r in m is calculated as o r v c r r (3) Table 1 Shape characteristics of potato cultivars and golf balls used in the experiments Cultivar Square mesh size, mm Shape factor Sante 2835 146 Arinda 3545 362 Marfona 3545 168 Golf balls 42C18 100 A shape factor S based on all three dimensions was introduced: S 100 l 2 wh (1) 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. 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 time of free fall t fall in s is calculated with ARTICLE IN PRESS ASSESSMENT OF THE BEHAVIOUR OF POTATOES 37 The gap in the duct has to be large enough for a potato x clear r c afii9825 release afii9853 x release Line A Line C Fig. 2. Process simulated by model, simulation starting 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 soil surface (free fall); r c , sum of the radius of the roller, thickness of the belt and length of the cup; x clear , clearance between cup and duct wall; x release , release clearance; a release , release angle ; o, angular speed of roller; line C, ground level, end of simulation to pass and be released. This gap x release in m is reached at a certain angle a release in rad of a cup passing the roller. This release angle a release (Fig. 2) is calculated as cos a release r c x clear C0 x release r c (4) where: r c is the sum in m of the radius of the roller, the thickness of the belt and the length of the cup; and x clear 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 t release in s needed to form a release angle a o is calculated as t release a release o r (5) Calculating t release 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 field speed of the planter, this gives the planting accuracy. y release v end t fall 0C15gt 2 fall (8) where g is the gravitational acceleration (9C18ms C02 ) and the final velocity v end is calculated as v end v 0 2gy release (9) with v 0 in ms C01 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 t release has to be added to t fall . 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 modified 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 visualise the behaviour of the potatoes in the transparent duct and to 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 potato passed the ground line. Standard deviation 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 u end in ms C01 . The initial vertical velocity of the potato u 0 inms C01 is assumed to equal the vertical component of the track speed of the tip of the cup: v 0 r c o r cosa release (6) The release height y release in m is calculated as y release y r C0r c sina release (7) where y r in m is the distance between the centre of the roller (line A in Fig. 2) and the soil surface. ARTICLE IN PRESS H. BUITENWERF ET AL.38 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 2C15ms C01 , the potato moves approx. 2C15mm between two frames, sufficiently 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 C01 (f pot 5, 6C17 and 8C13s C01 ) corresponding to belt speeds of 0C133, 0C145 and 0C156ms C01 . These speeds would be typical for belts with 3, 2 and 1 rows of cups, respectively. A fixed feeding rate of 400 potatoes min C01 (cup-belt speed of 0C145ms C01 ) was used to assess the effect of the potato shape. For the assessment of a normal distribution of the time intervals, 30 potatoes in five repetitions were used. In the other tests, 20 potatoes in three repetitions were used. Fig. 3. Laboratory test-rig; lower rightpart of the bottom end of upper rightsegment faced 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 confidence interval is equal to (100C0a)%. 3. Results and discussion 3.1. Cup-belt speed 3.1.1. Empirical results 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 C01 were 33C10, 20C15 and 12C17ms, respectively. the sheet metal duct was replaced with transparent acrylic sheet; by the high-speed camera 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 is increasing with the cup-belt speed, with CVs of 8C16%, 7C11% and 5C15%, respectively. 3.1.2. 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 0C1055m, 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 0C1025m for 300 potatoes min C01 and of 0C1041m for 400 potatoes min C01 . 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 0C1020m. The mathematical model Eqn (5) predicted a linear relationship between the radius of the roller (for r40C101m) 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 C01 . 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 0C1025m, which is probably the smallest radius technically possible, should have given a decrease in ARTICLE IN PRESS 0 . 035 0 . 030 f (x) 0 . 025 0 . 020 0 . 015 0 . 010 0 . 005 0 . 000 180 260 500340 Time x, ms 420 500 pot min 1 400 pot min 1 300 pot min 1 Standard deviation, ms 15 10 5 0 0 . 00 0 . 02 0 . 04 Radius lower roller, m 0 . 06 0 . 08 y = 922 . 1 x 17 . 597 R 2 = 0 . 9995 Fig. 6. 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 r40C101 m, K, measurement data; m, data from mathematical model; , extended for ro0C101 m; , linear relationship; R 2 , coefficient of determination ASSESSMENT OF THE BEHAVIOUR OF POTATOES 39 Fig. 4. Normal distribution of the time interval (x, in ms) of deposition of the potatoes (pot) for three feeding rates 80 64 48 Size of opening, mm 32 16 0 0 . 00 0 . 05 0 . 10 0 . 15 Time, s 0 . 20 0 . 25 0 . 36 m s 1 0 . 72 m s 1 0 . 24 m s 1 Fig. 5. Effect of belt speed on time needed to create opening Table 2 Time intervals between consecutive potatoes calculated by the model (cv. Marfona) Belt speed, ms C01 Difference between shortest and longest interval, s 0C172 17C16 0C136 29C14 0C124 42C18 35 30 25 20 y = 262 . 21 x 15 . 497 R 2 = 0 . 9987 standard deviation of about 75% compared to the original radius. 3.2. Dimension and shape of the potatoes The results of the laboratory tests are given in Table 3. It shows the standard deviations of the time interval at a fixed feeding rate of 400 potatoes min C01 . These results were contrary to the expectations that higher standard deviations 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. The normal distribution of the time intervals is shown in Fig. 7. Significant differences were found between the balls and the potatoes. No significant differences were found between the two potato varieties. The poor performance of the balls was caused by the fact that these balls could be positioned in many ways on the back of the cup. Thus, different positions of the balls in adjacent cups resulted in a lower accuracy of deposition. The three-dimensional drawing of the cup- belt shows the shape of the gap between cup and duct illustrating that different opening sizes are possible (Fig. 8). and the potatoes, demonstrated that the potatoes of cv. The mathematical model predicted the performance of the process under different circumstances. The model simulated a better performance for spherical balls compared to potatoes whereas the laboratory test showed the opposite. An additional laboratory test was done to check the reliability of the model. In the model, the time interval between two potatoes is calculated. Starting point is the moment the potato crosses line A and end point is the crossing of line C (Fig. 2). In the laboratory test-rig the time-interval between potatoes moving from line A to C was measured (Fig. 3). The length, width and height of each potato was measured and potatoes were numbered. During the measurement it was determined how each potato was positioned on the cup. This position and the potato dimensions were used as input for the model. The measurements were done at a feeding rate of 400 potatoes min C01 with potatoes of cv. Arinda and Marfona. The standard deviations of the measured time intervals are shown in Table 4. They were slightly different (higher) from the standard deviations calcu- ARTICLE IN PRESS Time x, ms H. BUITENWERF ET AL.40 Fig. 7. Normal distribution of the time interval (x, in ms) of deposition of the potatoes for different shape factors at a fixed feeding rate 0 . 050 0 . 045 0 . 040 0 . 035 0 . 030 0 . 025 0 . 020 f (x) 0 . 015 0 . 010 0 . 000 245 255 265 275 285 295 305 315 325 335 0 . 005 Marfona shape factor 168 Arinda shape factor 362 Golf ball (sphere) shape factor 100 Table 3 Effect of cultivars on the accuracy of plant spacing; CV, coefficient of variation Cultivar Standard deviation, ms CV, % Arinda 8C160 3C10 Marfona 9C192 3C15 Golf balls 13C124 4C16 Arinda always were positioned with their longest axis parallel to the back of the cup. Thus, apart from the shape factor, a higher ratio width/height will cause a greater deviation. For cv. Arinda, this ratio was 1C109, for cv. Marfona it was 1C115. 3.3. Model versus laboratory test-rig Arinda tubers were deposited with a higher accuracy than Marfona tubers. Analysis of the recorded frames Fig. 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 its release found. So, to provide more room for reductions in the cup-belt speeds while keeping a high planting accuracy it It is recommended to redesign the geometry of the cups and duct, and to do this in combination with a smaller roller. Acknowledgements using machine vision. Transactions of the ASAE, 38, ARTICLE IN PRESS Table 4 Differences between the standard deviat