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If ... 2... fi....v__..:.,.u...s . .ca..(~ {.11. : cpl}... . . ,. 1 . _ A. . tamww‘piy .r. wx£rhfivtbsrzfv¥w€i it i .. . , . . _ 1- fibriidgfip. hi;s5§. 05> 11> {b °C C1: 02: 03 LIST OF SYMEIS Impact location Area Pendulum drop angle Pendulum rise angle after impact hmpact location Impact location Chain batch Length Cosine lkmperature NUmerical values given to the petiole response, zero, one—half and one, respectively Impact location Distance between the beet rows Disc Maximum diameter of beet Energy Apparent modulus of elasticity Energy loss due to rotation of the defoliator Energy loss due to translation of the defoliator Efficiency of defoliation X degree degree centimeter degree Celsius “E“S decimal I?! Q I Ed [:11 H- ' (m) 00'?! '11 m 5‘ mm EFL—‘(E‘NHOH M1 , M2 Total mean efficiency of defoliation (average of means of four locations) Impact energy Modified impact energy Total mean impact energy (average of means of four locations) Force Centrifugal force Shear modulus of elasticity Gravity acceleration Disc thickness Height Mass mment of inertia about 0 Energy Bulk modulus of elasticity Mass Distance of beets in the row length of beet samples Mass Mass of the disc and a batch of chain, respectively Pressure Total mass of the defoliator Length length Time Force Total number of tests for each impact location each day xi decimal meter millimeter millisecond newton poo/N Subscripts A 9: Cup-DOW Period of pendulum free oscillation Transducer sensitivity Distance between the impact center and the center of rotation of the pendulum Angular velocity Distance from the centroid of the chain to the disc center Distance from the center of gravity of the pendulum to the center of rotation Disc radius Time Sine Temperature Defoliator forward linear velocity Linear velocity of the pendulum at impact point impact locat ion apparent average impact location impact location impact location defoliation drop center of gravity xii S picocoulombs per newton m revolution per minute m second i impact i(m) modified impact 3' impact locations A, B, C or D max maximum 0 center of rotation r rise rr radial direction zz vertical direction 09 circumferential direction { Greek sflls ‘Y m Angular velocity rad/s if A Difference — II 3.14 _. 8 Strain —— 0 Normal stress Pa Tmax Maximum shear stress Pa v Poisson's ratio —— I . INTRODUCTICI‘I The sugar beet (Beta Vulgaris L.) has to be topped or defoliated before it is delivered to the processing plant for the extraction of sugar. Improper defoliating or topping is one of the major losses of Sugar in the beet processing industry. Defoliation consists of removing the foliage of the beet plant with rotating steel and rubber flails. Conventional defoliators have the flails hinged radially to rotating drums. The beet petioles are ruptured from the beet by the impact of the rotating flails, Figure 1. Different types of defoliators have been developed to defoliate the sugar beet. Conventional defoliators leave behind beets which are partially de— foliated, inverted and With crown cut-offs. Tne beet petioles are struck from different locations and directions by the defoliator during harvest. The objectives of this study were to investigate the behavior of the beet petioles when impacted and to study the material properties of the beet root. The overall objective was to develop defoliator desigi criteria based on the mechanical properties of the petioles and beet which would reduce the problems associated with the conventional defoliators. The work reported in this thesis consists of six major parts: 1. The apparatus and instrumentation used in conducting the experiments . m1 ° charge Charge Storage ‘t-w-fi'“;’:__ Pagplifrer d . t - - e 10 e un er ac gill—b 2:113:10“ ‘ ' Impact elementmp Sugar beet The clapping device Base Figure 2. The Schematic Diagram of the Instrumentation. 4 6 a— .1... A 4.?6 Pivot int > Ball bearing /‘ Indicator ———/ 15 l 24.13 Marker e 45 Center of gravity e k1 1'94 -.1.9 Force transducer .I. Figure 3. The Schematic Diagram of the Impact Arm. (All distance values are centimeters .) Impact velocity , m/s Drop angle , degree Figure 4. Comparison of Theoretical and Measured Impact Velocities . 10 where M = mass of the pendulum g = drop height of the pendulum which from the geometry, Figure 2, is given by h=rg (l-CosAd) (3) where r g and A d are the distance from the center of gravity of the pendulum to the center of rotation and the drop angle of the pendulum, respectively. The mass moment of inertia, I about point 0, the center 0, of rotation is: 2 r Io = 3.35.2 (4) 4112 where P is the small amplitude free oscillation period of the pendulum. Replacing h and IQ of equation (2) with equations (3 and 4), and sub- stituting it in equation (1) for w, the linear impact velocity at the impact point becomes ———1'— <1 - Cos Adm / - (5) The pendulum was calibrated for different drop angles to determine the effect of air, bearing and marker resistance on the operation. The calibration results are shown in Figure 5. The impact signals were sensed by a Kistler Model 912 quartz force transducer with a charge sensitivity of 10.83 PCb/N (pioo columb per newton). The force transducer was protected against any side contacts. The signals were picked up by a Kistler 121 M(5) cord, amplified and 11 Theoretical Measured Drop angle , degree O 1 I T I 0 15 30 45 60 Rise angle , degree Figure 5. Calibration of the Pendulum for the Effect of Air, Marker and Bearing Resistance . 12 displayed on an oscilloscope screen . The charge amplifier was a Kistler Model 504D Dial-Gain, with ranges of 4.448 to 22.24 kilonewton per volt and transducer sensitivity of .224 to 2.24 pCb/N. VA tektronix type 549 storage oscilloscope was used to dis- play and store the signals. Pictures were taken from the stored signals using a Hewlett Packard Model 196 A oscilloscope camera . The approximate velocity at impact was measured using two electro— magnetic pickups installed 40 mm apart. The magnetic pickups were connected to a Beckman Model 6040 A electronic counter. The air temperature was measured with a thermometer having a resolution of 1 degree Centigrade. The internal beet temperature was measured by inserting the same thermometer to the center of the beet once it had been pierced. The moisture content of the petioles was measured using a Precision Scientific oven Model 625 which dried the petioles at 105 °C for 26 hours. The percent of the total dissolved sugar of the beets was measured by an A0 Model 10406 refractometer with a scale division of 0.1 and an accuracy of 0.05 percent . IV. METHDDANDPIDCEDURE Certain assumptions were made when designing the experiments of this investigation because the beets were tested under laboratory conditions rather than in the field. The assumptions were justified on the basis of observations and the testing time. The assumptions were as follows: 1. The change in turgidity of the beet petioles during the testing period was assured insignificant . It took approximately five minutes to return from the sugar beet field and fifteen minutes to perform the tests on the petioles. The petioles selected for impacting were considered to have a uniform size. The petioles located at the center of the crown were eraller and weaker than those on the outer edges . These petioles along with cracked petioles were not used in the experiment. The clamping of the beet was assumed to provide a support similar to that of the ground. The resistance of the petioles to impact was low and no vibration or movement of the beet (hiring the impact was visible . Each day during the Michigan sugar beet harvesting season , October 12 through November 10, one beet was carefully removed using a shovel and taken to the laboratory. 13 14 The sugar beets were hand cleaned to remove extra soil and any debris and leafy parts which.would.have*obstructed the tests were eli- minated. There was always more than enough petioles left to conduct the experiments. A thermometer was inserted into the pierced beet to deter- :mine its temperature. The beet with a petiole in position for impact was fixed in a vise, Figure 2, Four locations A, B, C and D involving two different distances along the petiole were impacted, Figure 6. Radially oriented locations, A.and.C, were perpendicular to the tangential load application locations, B and D, respectively. locations A and B were 127 m away from the crown of the beet, and locations C and D 25.4 mm. The petioles became thinner beyond the 127 mm location , and were too flexible to break under an impact load. The lower level of 25.4 mm was a. minimum because the impact arm made contact with the'beet crown and other petioles below this point. The tests at the different locations were performed using different petioles of a single beet to eliminate differences between beets and to reduce the time between measurements. Once the'beet was clamped in the desired.position, the pendulumlwas . raised 60 degrees from.the zero potential energy position and released. The 60 degrees drop angle gave:mm > D gs . \I \\ a; s) \ a; \ . ss /\ ~ \ s \ a . 1 mm . O \ . ~ a 5’ .4 es ’ > \s I \\~ / s a \ I s a \ I II \\ i s ’ \ I x a f x A Q /I\\ a~ a I \ It \ ’o/ a \ ¢ (s < If \\ 1’ (s CA emof ‘ Karena 1012 c1111 6028 3382a: wage 22.2. 30:8 22» 53 meofieocq 220:3 poem mo 3.88m young one yo 53.39.60 . em magma .2 8:88 mafia mean .25. 8 mm on nu ma m H ‘1 p P k Coo 693 86 .. «and n 3m . 693 mood .. Sod u mam T o 1.66 Atacama Sod .. «Ed a cam 65: mood .. 89o u 3e lo; emoc ‘ABa'eue 1012an 45 .H 6028 $398.8: mange a as o .m a 20383 mo mm. $8.829 poems—H omenm>< 05. 90 6:95. Hamocmo 05. .mm cash 3 .8988 Sta mean .959 on we om ma OH m H A . _ _ r . _ o. O 6&3 wood .. mac n m I ad I DA smog“ ‘ASJeue reading emeAv 46 (D '3 O "'3 E; . : ii = 0.331 + 0.027 (°C) g 5 0. - 3% 0 0. F» 1. 5 10 15 Beet terperature, °C Figure 26. Variation of the Total Mean Impact Energy, iii, with the Temperature of the Tested Beets. 47 The energy—temperature relation, shown in Figure 26, is true only for the range as indicated. Higher temperatures dry the petioles. They can then be removed with less emery. The petioles freese at lower temperatures producing a form of stiffness requiring greater amounts of emery for their remval. 5 . Nbdified Impact Emery The impact emery developed earlier, does not give a true picture of the defoliation process . A low impact energy is generally associated with a low efficiency of defOl iat ion because the petiole has deflected and not broken . Thus additional energy would have to be input to complete the defoliation process . _ An impact emery term which includes the efficiency cf defoliation was calculated by multiplying the value- of the rise angle, Ar’ by Ed' The result was. called the modified impact energy, E. 1(m)‘ The rise angle corresponding to the petiole which was Lmdameged after impact was considered to be zero because the emery of the pendulum was lost to the displacement of the petiole rather than remving it. The modified impact emery was obtained by multiplying the Ar of ' equation (11) in Ed, which resulted =2.3[CosAr. E.-O.-5], j=A,B,CorD (12) Ei(m)J' J dJ 48 5. l The effect of impact 'lOCat‘ion on the modified impact energy The results obtained for the modified impact energy indicated that differences exist among the mean values for locations A, B, C and D as shown in Figure 27 . The difference of the modified impact emery between locations A and C was not significant at 99.95 percent confidence level. However, the differences between other locations at the same confidence level were significant as can be seen from Figure 28. The highest modified impact emery occurred at A and lowest at D with the other locations in between. It would be misleading to justify the differences in the modified impact emery for the four locations without considering the influence of the defoliation efficiency on the impact energy . As discussed earlier when considering the impact emery, the modified impact emery values for locations A and B should have been much lower because of their higher flexibility, but as was indicated in the analysis of the efficiency of defoliation, location A bad the lowest efficiency meaning high rise angles after impact which in turn is an indication of less energy absorption. If the objective is to consider the emery that has caused heavy damage, a break or crack, then the ordering of Figure 28 can be employed. The discussion suggests that it would require less impact emery for location D than the other locations if the breakage of the petioles is the main concern. 49 __. H .1 i(m) = 0.881 Mean modified impact emery, joule o 01 l o b d fi Location Figure 27. The Mean Nbdified Impact Emery Deviations from the Total Mean, Ei(m)’ for the Four Different Impact Locations. 50 0.0 Figure 28 . 0"”0 J—b 0.5 V 1. Modified Impact Emery Averages Ordered from the Lowest to the Highest for Different Impact Locations, Joule. 51 5 .2 Variation of the modified impact energy during harvesting period The values of the modified impact energy varied during the harvesting period, Figures 29 and 30 with their general trend of variation in Figure 31. The results of the modified impact emery, as shown in Figure 31 , decreased for locations C and D and increased for locations A and B. The variations in the values of the impact emery were less than those of modified impact emery for all locations which is due to the contribution of the variation of Ed in equation (12) . 52 so is $828 messages warns m sea < 28388 a .388 885 .8388. one eo 832.3, .8 obese 2 noooooo seems uses .82. mm ON ma OH m . p — _ o.o rm.o armor ‘ifireue roadm'; pernpow 53 dogma assumes/Ham page G use 0 meoflnoos so...” Asia .888 e895 88.."er ofi so someone, .8 288 NH aoooeoc note uses .25 mm mm as 2 2 e ‘ . _ _ p C.O . m .o armor ‘ 5813118 1:73qu .oofloe mofiuofie: one unease sees. 38:8 .385 so? mooa e88 gamers .Soa Ho 088 e89: 888% one .6 8838.8 .8 882 2 e388 goose mass .25 as: 1\.\\. $.88 mood I Ed u n83 mood + 86 u moses Q :11 <11 o.o rod CA 8.33 nuanced .. 2o; u oases « $83 89o + some n «Assam stoop ‘Afireue 10’9an VI . DEFOLIA’IUR DESIGN CRITERIA Sugar beets processing plants around the world require the foliage and a certain port ion of the beet crown to be removed before it is delivered to the factory. The»requirements on the amount of material renrwed.depends on regional regulations. crownznamnnfl.nay’vary from 'the lowest leaf scar (25) to the very top portion of the crown. Recent studies in the U;S.A. (7 and 32) indicate that cutting the crown is not desirable because of the exposure of the beet flesh to the environment and.the loss of sugar and.weight loss during storage. 3 Conventional defoliators with.rubber and steel flails are designed to remove the foliage and some portion of the crown . . These defoliators leave behind beets with brdken tops, inverted beets and partially de— foliated beets all which contribute to the loss of sugar, Figures 32 and 33 . 'Dhe Objective of this discussion is to develop a design criteria for a defoliator which renoves the foliage from the crown without breaking the»roots. The design criteria discussed.herein was developed assuming average conditions for the beet and foliage. Canparison of economy, efficiency or other factors with the conventional defoliators will have to be made under field conditions. This part is left as a future study. The laboratory studies showed that a higher percentage of petioles were removed when impacted close to the crown (location D). An impact 55 Figure 32. Broken Beet and Poorly Defoliated Petioles (Numbers 1 and 2) as Compared to Proper Defoliation (Number 3). 57 Figure 33. Broken Beet and Poorly Defoliated Petioles by Conventional Defoliators. 58 force of approximately 11 N with an impact velocity of 2.45 m/s was required to remove an average petiole. The average amount of energy required to remove a petiole was 0.6 joule. A higher percentage of the petioles were removed when they were turgid. These results and constraints will have to be taken into consideration in designing a defoliator . A rotary disc, d, with a total mass, M1, radius r; and thickness H was devised, Figures 34 and 35. Groups of chains, c, with a total mass M2 for each group and an average radial distance of ra from the center of rotation, hinged to the periphery of the disc as the impacting arm. A hollow shaft similar to those in the conventional defoliators could also be used instead of the disc, Figure 36. The preference of the disc over the shaft or vice versa depends on the results of their operation in the field. i The rotating disc can either be carried by a skidder shoe or mounted on a tractor and powered by a hydraulic motor or by the power take-off . There are three major constraints imposed on the defoliator: 1. An average force of 450 N is required to tear off the petioles of one beet. The range varies between 80 and 700 N (19). 2 . The horizontal component of this force which attempts to over- turn or rotate the beet should average less than 200 N for crowns greater than 50 mm above the ground level (19). 3. The lower and upper limits of the disc angular velocity are limited by the minimum centrifugal force to keep the chain links nearly straight and by the maximum striking force that the beet root can stand without being damaged. The upper limit depends on the total mass of the rotary mechanism M , the 59 D @ c — Chain batch . d - Disc - l dr - Maximum diameter of beet Top View “ax . I D - Distance between the beet rows . H - Average height of the beet above I the ground level, also thickness . of the disc I L — Distance of the beets in the row . ra - Distance from the centroid of l the chain to the center of ' rotation I r1 - Radius of the disc _.L 7 i c V f - Forward velocity H 4,40 l (1 Ground level .1 I ' Beet : l \ 1 o ‘ I \‘ ’ V Side View Figure 34. Schematic Diagram of Rotary Defoliator. b . After defoliation Figure 35. The Prototype Model Defoliator using Chain as an Impacting Arm. 3.. During defoliation b . After defoliation Figure 36. The Prototype Model Defoliator using Chain as an Impacting Arm. 62 distance from the centroid of the impacting chains to the center of rotation, ra, and the number of the impacts per 1mit of time. An angular velocity of approximately 200 rpm was determined to be the limiting value for the prototype model (Mt = 9.5 kg and r21 = 0.39 m), in order not to break the crovm while removing the petioles. The lower rpm limit (approximately 50 rpm for the prototype model) is determined as follows . The centrifugal force is equal to mass times the normal accelera- tion of the disc which is equal to ra m2. This force has to be greater than the weight of the chain batch Mzg in order to keep the chain links nearly straight, thus 2 F =M2ram C > M2 g (13) The relation between angular velocity to and revolution per minute is m = 216-10391 (14) Replacing (14) for u) in (13) gives 60 1 2 rpm > 'gff- (%') (15) a where F = centrifugal force, N M2 =mass of abatch of chain, kg distance from the centroid of the chain batch to the center .1 ll of rotation 63 rpm = revolut ion per minute g acceleration due to gravity = 9.8 111/32 m = angular velocity, rad/s The kinetic energy of the rotating disc at the impact surface is E=E1+E2 (16) E=-]-’- r2m2+-l— v2 (17) 2Mt a 2Mt f where E = kinetic energy of rotating mass at a distance ra from the center of disc rotation, joule til-1 ll energy loss due to rotation of the defoliator, joule [2121 to II energy loss due to translation of the defoliator, joule total mass of the defoliator, kg .5 ll vi = forward velocity of the defoliator, m/s The energy stored in the disc will have to overcome the energy loss due to the removal of the petioles (an average 24 joules per beet) and the energy loss due to the friction of the chain against leaves (the kinetic coefficient of friction of steel against leaves and beet top was determined to be in the range of 0.6 to 0.7 (19)). Energy will also be lost because of the contact of the defoliator with the ground and vibration of the mechanism. Beets were held by hand and by a vise in the path of the impacting chain arms in the laboratory tests of the prototype defoliators, Figures 35 and 36. The horizontal defoliator, Figure 35, had a higher total mass 64 and greater vibration compared to the vertical defoliator, Figure 36. The horizontal defoliator, however, left less remnants of petioles on the crown after defoliation. Defoliation process was observed for differ- ent disc angular velocities and impacts per 1mit of time concerning the mechanism shown in Figure 35. Impact velocity, impact per unit of time and the mass of the chain batch were the determining factors in removal of the petioles. With the disc angular velocity 200 rpm and 0.2 kg chain mass the petioles were removed wittout severely damaging the beet in approximately 10 seconds . Increasing any of these factors caused crown damage in the form of skinning, flesh removal and breakage. VII. SGIE PHYSICAL PRCIPEIEH‘IES OF THE SUGAR BEEP m A sugar beet experiences mechanical loadings beginning with defolia- tion and ending when it is processed. The resulting damage can be ex- ternal or internal. External injuries as recorded by Precht e£_a_l_. (1976) .can occur as crown cut-off, root tip breakage, existence of a gash on one side, cut—off chips from the other side and overall skinning. All of these injuries contribute to the loss of sugar. Internal damage, not evident to the eye, such as crushed or cracked tissues may also exist . There has been very little work performed on determining the basic mechanical properties of the sugar beet such as its modulus of elasticity, Poisson's ratio and the type of failure under loading. These are essen- tial information in determining the relationships describing the failure characteristics of sugar beet under loading. Equations that have been developed to score sugar beet injury resulting from free fall weight tests do not provide an understanding of the type of the failure or the stress level developed within the material . The objective of the following experiments was to determine some of the mechanical properties of the sugar beet root for different loading orientations and sample sizes . The properties which are determined were the apparent modulus of elasticity, Poisson's ratio and the average max- imum shear stress at failure for a cylindrical sample. 66 l . Instrumentation Three dies with spacer plugs, as shown in Figure 37, for three different size samples were constructed. The samples were prepared as needed. Four samples were cut by a sharp blade for each size from two orthogonal direct ions. Two of the samples were loaded while restrained (in a die), and the other two loaded while unrestrained. All the loadings were applied using an Instron testing machine with a load cell of maximum capacity of 889.6 N which was calibrated using standard weights. The cross head speed of the Instron was 0.84 E—3 m/s. 2. Method and Procedure Tests were performed each day, from October 8 until November 10. All tests were conducted on one beet; the same used in the defoliation studies . Samples were taken from the middle part of the root (variety US 320) . Three different size samples were taken from each of two per— pendicular cross sect ions of the root, Figure 38. The samples were cylindrical in shape with diameters and lengths of 12.7 and 12.7 mm, 19.05 and 19.05 mm, 25.4 and 25.4 mm, respectively. These samples were designated as A, B and C. The two orientations from whiCh the samples were out were vertical and horizontal . The orthogonal direct ions were chosen because of apparent difference in the orientations of the fibers as shown in Figure 38. 67 Load Cylindrical un- restrained sample a . Unrestrained Spacer plug Restrained cylin- drical sample. Spacer plug 1’— Base plate b . Restrained Figure 37. Axial loading of Unrestrained and Restrained Beet Samples. Figure 38. The Orthogonal Directions of Load Application. 69 The measured parameters were the compressive force that caused failure of the sample, the apparent modulus of elasticity, Ea’ and the Poisson 's ratio , v, for different orientations and sizes of the beet samples. The apparent modulus. of elasticity was determined from the slope of the force-deformat ion curve at a level where the curve was approximately linear, Figure 39 . The stress was obtained by dividing the compressive force by the original cross sectional area of the sample and the strain was determined by dividing the deformation by the original length of the sample. Utilizing the Hooke's law (stress in a bar in tension or compression in the linear elastic region is equal to corresponding strain times by a constant of proportionality known as the modulus of elasticity), the ratio of the stress to the corresponding strain re- sulted in apparent modulus of elasticity. Different methods have been employed by the previous investigators to determine Poisson's ratios of agricultural products (Hughes and Segerlind, 1972 and hbhsenin, 1970). Because of simplicity, the die test method presented by Hughes and Segerlind for apples , peaches and potatoes, it was utilized in this study to obtain Poisson's ratio. In this method the cylindrical samples of material are loaded axially one unrestrained and the other restrained in a die as shown in Figure 37 . The slopes of load-deformation curves at a certain stress level where the curves were approximately linear, provided a measure of v . Assuming the specimens as elastic and isotropic material, for an unrestrained sample in polar coordiantes, the triaxial stress equations are 7O A 1000 _ k Restrained sample Point of sample failure Unrestrained sample m z 93“ H 500 - :2 0 l r I I l I 0 5 10 15 20 25 Sample deformation , mm Figure 39 . Typical Load—Deformation Curves for Cylindrical Samples of Sugar Beet Root. 8 _ 02.2 -v (on. + 090) 18 ZZ - E ( ) 0 - v (o + c ) 8co = 99 E rr ZZ (19) e _Grr-v(oee+ozz) 2 rr - E ( 0) where 522’ err’ 809 and Gzz’ Grr’ Gee are strains and stresses in vertical, 2, radial, r, and circumferential, 0, directions, respectively. For a restrained sample, the strains in 0 and r directions become zero. Therefore, equations (l8), (l9) and (20) when combined, for this case, lead to the following stress-strain relation ezz _ 2 v2 E(3-z;)-(1-1_v) (21) where v = Poisson's ratio = modulus of elasticity, and is equal to g=PA 8 AL L’ axial compressive load, N Pa D> "U til t1! ll original cross sectional area of the sample, 1112 F ll deformation corresponding to the load P, m II" II initial length of the sample, m To determine the value! of v from equation (21) the values of E and §_2z_ were determined from the slopes of the load-deformation curves, zz 72 Figure 39 . The slope of the unrestrained curve at a point where it was approximately linear , yielded the value of E a and the inverse of the slope of the restrained curve, at the same point , gave the value of For an elastic and isotropic material E and v are related to shear modulus of elasticity, G, and bulk modulus of elasticity, K, by E G = 2"“(1'4v) (22) E K=3(l-2v) (23) The maximum compressive stress was determined by dividing the compressive force at failure by the original cross sectional area of the sample, from which the maximum shear stress was obtained using the following equation max _1 T -§GZZ ' (24:) The above equation is obtained using the three dimensional Mohr's circle for the uniaxial loading. 3. Summary of the Results The average values of apparent modulus of elasticity , Poisson ' 5 ratio and maximum shear stress for 200 samples were determined to be Ea = 11.531 14%, v = 0.39 and Tm = 1.250 MPa, respectively. 73 There were insignificant differences in the mean values of E a and Tmax for different loading directions and sample sizes except size A which had different values of apparent modulus of elasticities for the two perpendicular directions. This comparison was at a 0.999 confidence coefficient. At the same level of confidence the two orthogonal directions had.insignificant differences iniflmamean values of Poisson's ratio, however, different sample sizes showed significant differences. Observations on the sample failure for different sample sizes and loading directions indicated a common type of failure. The samples failed along the plane making approximately 45 degrees with the axial loading direction, Figure 40. This type of failure indicates that the :material has failed in shear’along the plane on which the shear stress had alnaxhnmniwihme. The results of variations of the daily average values of Ea! v andrmax during the harvesting season as shown in Figures 41, 42 and.43, respectively, indicated that the variation of Poisson's ratio during harvesting period was insignificant, while the change in the values of Ea and “I:max for the same period was significant. The values of Ea’ v andrmax are tabulated in Tables 1, 2 and 3. The values of E a had an increasing trend, which means the material became stiffer as the time progressed. Also, the values of Tm had an increasing trend. 74 Figure 40. Failure of Cylindrical Sample under Axial loading. 75 Apparent modulus of elasticity, MPa ° Ea = 9.765 + 0.098 (days) D 5 -I 0 II. I I I I I I J 1 5 10 15 20 25 30 35 Time, days after October 8 F Figure 41. The Trend of Variation of Apparent Modulus of Elasticity of Sugar Beet during Harvesting Season. 76 A m 0.5- \) = 0.380 + 6.7E—4 (days) i O p o 0 e . o . 'H o g o . . g . . . m U) ‘ - v e g . o ' ° . e . e ,3 0.25.1 4.) R _m o 8 m -H a 0 0 ' 1 I I I I I f. l 5 10 15 20 - 25 3O 35 Time , days after October 8 Figure 42. The Trend of Variation of Poisson's Ratio of Sugar Beet during Harvesting Season . 77 3'- Tmax = 1.041 + 0.011 (days) Maximum shear stress, MPa to l I 20 25 30 F. 01% H O H 01 Time, days after October 8 Figure 43. The Trend of Variation of Maximum Shear Stress of Sugar Beet Samples during Harvesting Season. 78 Table 1. Tabulation of the values of apparent modulus of elasticity for different sizes and orientations of the sugar beet samples, starting OctOber 8 as number 1, MPa. Sample size1 A B C Loading orientation2 V H V H v H Test Number 1 8.778 7.980 —— —— 4.877 7.980 2 11.705 10.328 —— - 7.480 10.973 3 10.328 9.754 -— —- 4.620 10.973 4 11.434 10.973 -— - 11.161 10.364 5 9.754 10.328 -— - 10.973 12.541 6 10.328 9.754 —- -— 8.778 9.754 7 9.241 10.973 - - 7.980 12.541 8 11.705 10.328 - 9.754 9.754 9 10.973 9.241 -— -— 14.631 9.754 10 12.541 11.705 8.360 9.754 6.753 10.973 11 9.241 8.360 11.705 10.641 12.541 12.541 12 10.328 10.328 9.754 11.705 12.541 12.541 13 13.506 13.507 10.641 14.631 21.947 17.557 14 13.506 9.754 16.721 9.754 9.754 10.973 15 9.241 9.241 8.361 19.262 7.980 14.631 16 9.754 7.315 10.641 9.004 10.973 17.557 17 10.973 10.328 10.641 11.705 7.315 8.778 18 12.541 10.328 13.005 13.005 10.973 10.973 19 11.705 9.754 14.631 11.705 12.541 14.631 20 10.973 11.705 ' 7.803 9.754 12.541 12.541 21 10.329 8.778 9.004 9.004 14.631 12.541 22 13.506 12.541 10.641 9.741 17.557 14.631 23 9.754 9.241 9.004 19.508 9.754 9.754 24 12.541 10.328 9.004 13.005 12.541 17.557 25 13.505 10.378 11.705 8.361 14.631 10.973 26 12.541 10.973 13.005 11.705 21.947 12.541 .27 11.705 10.973 9.754 10.641 12.541 14.631 28 10.328 10.328 9.754 9.754 10.973 9.754 29 12.541 9.241 9.754 13.005 9.754 7.981 30 14.631 10.328 13.005 13.005 14.631 17.557 31 12.541 11.705 14.631 11.705 17.557 12.541 32 11.705 9.754 13.005 14.631 14.631 10.973 33 14.631 13.505 14.631 16.721 10.973 17.557 34 14.631 11.705 11.705 16.721 12.541 12.541 35 11.327 11.705 11.147 12.321 14.631 13.505 1The sizes A, B and C correspond to the cylindrical samples with diameters and lengths of, 12.7 and 12.7 m, 19.05 and 19.05 mm, 25.4 and 25.4 mm, respectively. 2v and H are vertical and horizontal loading directions, respectively. 79 Tabulation of the values of Poisson's ratio for different Table 2. sizes and orientations of the sugar beet samples, starting October 8 as number 1, dimensionless. Sample size1 loading orientat ion2 Test nmber mmmmpmmmmmwmmwwmmmwmwmmn mmwmmmmmmw 00000000000000000000000000000000000 mwnmwmwmmuwmwmmwwmmmmmmmmwmmmmmmmmm 00000000000000000000000000000000000 _“u__i__.meeenmsnmnnmnrsmnrsns.onr. 00000000000000000000000000 ___l_____rno%noor nonoooronnnrornno 00000000000000000000000000 mmmnnmm mmmmmwmmmnmmm mammmmnmmmmmm 0000 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO mammmwnn mwmmmmmmmnwmmmmmmmmmmmmm m OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 00000000000000000000000000000000000 123456789mummmmmummmmmmmr%m%%wmmmmm 1The sizes A, B and C correspond to the cylindrical samples with diameters and lengths of 12.7 and 12.7 m, 19.05 and 19.05mm, 25.4 and 25.4 mm, respectively . 2V and H are vertical and horizontal loading directions, respectively. 80 Table 3 . Tabulation of the values of maximum shear stress for different sizes and orientations of the sugar beet samples, starting October 8 as number 1, MPa. Sample size1 A B C loading orientat ion2 V H V H V H Test number 1 0.825 1.053 - - 1.097 1.141 2 1.062 1.062 -— - 0.992 1.931 3 1.615 1.537 - - 1.281 1.698 4 1.382 1.483 -— -— 1.104 1.163 5 0.912 1.141 - - 0.833 1.141 6 1.018 1.053 -— - 0.967 0.790 7 1.579 1.544 - - 1.360 1.470 8 1.176 1.053 - -— 0.820 0.816 9 1.000 1.141 -— - 0.899 0.746 10 1.351 1.492 1.248 0.995 1.163 1.240 11 1.457 1.501 1.112 1.209 1.163 1.229 12 0.860 0.921 1.092 1.097 0.790 1.042 13 1.141 1.141 1.092 1.170 1.064 0.943 14 1.123 1.079 1.209 1.287 1.141 1.471 15 0.895 0.983 0.995 1.172 0.932 1.251 16 0.921 0.983 0.975 1.014 0.976 0.987 17 1.035 1.070 0.858 1.131 0.557 0.592 18 0.842 0.930 0.897 0.839 0.878 0.838 19 1.597 1.615 1.424 1.521 1.624 1.481 20 1.422 1.457 1.482 1.521 1.571 1.712 21 1.667 1.474 1.443 1.580 1.514 1.580 22 1.430 1.571 1.295 1.521 1.349 1.624 23 1.334 1.316 1.287 1.073 1.240 1.459 24 1.343 1.176 1.424 1.209 1.744 1.668 25 1.053 1.109 1.073 0.936 1.229 1.196 26 1.193 1.404 1.151 1.619 1.426 1.679 27 1.272 1.158 1.092 0.975 1.053 1.295 28 1.369 1.316 1.112 1.326 1.631 1.185 29 1.193 1.316 1.151 1.272 1.152 1.338 30 1.773 1.913 1.443 1.424 1.351 1.431 31 1.562 1.509 1.365 1.560 1.246 1.338 32 1.611 1.702 1.502 1.248 1.492 1.387 33 1.632 1.615 1.287 1.580 1.624 1.606 34 1.667 1.702 1.619 1.541 1.646 1.524 35 1.439 1.492 1.502 1.248 1.525 1.343 1The sizes A, B and C correspond to the cylindrical samples with diameters and lengths of 12.7 and 12.7 m, 19.05 and 19.05 mm, 25.4 and 25.4 mm, respectively. 2V and H are vertical and horizontal loading directions, respectively. VIII. (DNCLUSIQIS The following conclusions were derived from this study: 1. There were intermediate peaks in the force-time curves after failure of the petioles (the highest peak). No intermediate peak was found before the failure. It was thought that the skin of the petiole opposite to the impacting side to be responsible for the secondary peaks. Four different locations on the petioles were impacted. Each location responded differently to the impact . When the petioles were struck close to the crown and in tangential direction (designated as location D), a maximum number of petioles failed (100 percent efficiency of defolia- tion) . A higher impact energy was required for this location than the other locations. The percent removal of the petioles and the energy necessary to remove them varied during the harvesting season , with a de- creasing trend from the beginning to the end of the season. Approximately 24 joules of energy was sufficient to defoliate an average beet . The petioles were removed by applying about 440 newtons of impact force per beet , with an impact velocity of 2.45 m/s. Higher impact velocities will be necessary if the crown is impacted also (as occurs under normal field operations). 81 10. 11. 82 Among the measured parameters (total dissolved sugar, air and soil temperatures, air and petiole moisture contents) the beet temperature had the highest correlation with the percent of the reroval of the petioles and the impact energy to remove the petioles. Visual observation indicated that turgidity of the petioles was an important factor affecting their mechanical behavior. A higher efficiency of defoliation was obtained when the petioles were turgid and stiff. A higher percentage of the petioles were removed for all impact locations before overnight freezing and daytime thawing occurred in the field. A rotary design criteria, using chain links as impact elements , was designed and a prototype model was made and tested in the laboratory. The results regarding the foliage removal were promising. Further study on the field tests of the suggested design has been recommended. The apparent modulus of elasticity, E a’ maximum shear stress, 1' and Poisson's ratio, v, of the beet roots were determined max’ for three different sizes of cylindrical samples in two ortho- gonal direct ions. The average values of E a’ T max and v for 200 samples were evaluated to be 11.531 MPa, 1.250 MPa and 0.39, respectively. All samples regardless of size and loading orientation failed in shear along the plane making approximately 45 degrees with the axial loading direction. 13. 14. 83 There were insignificant differences in the mean values of E a and Tmax for different loading directions and sample sizes except size A which had different values of apparent modulus of elasticities for the two perpendicular directions. Poisson's ratio was not a function of sample orientation but different sample sizes showed significant differences. The change in the values of v during the harvesting season was insignificant, while the values of Ea and TM had an increasing trend. N 10. 11. 12. IX. LIST 05‘ REFERENCES Akeson, W. R. , 1973. Environmental factors influencing storage loss (tapping procedure). Proceedings of the Beet Sugar Development Foundat ion. Conference held in California pp . 67-74 . Akeson, W. R., S. D. Fox and E. L. Stout, 1974. Effect of topping procedure on beet quality and storage losses . Journal of the A.S.S.B.T. (American Society of Sugar Beet Technologists). 18(2) :125-135 . Alizadeh, H. , 1976. 7 Sugar beet topping. Unpublished technical problem report, Department of Agricultural Engineering, Michigan State University, East lensing, Michigan. Bernacki, H., J. Hanan and Oz. Kanafojski, 1967. Agricultural Machines; Thme and Construction, Vol. 1, Published by PWRiL, Warsaw, Poland, 883 p. Bittner, D. R., H. B. Manbeck and N. N. Mohsenin, 1967. A method of evaluating cushioning materials used in mechanical harvesting of fruits and vegetables. Trans. of ASAE., 10(4):7ll-7l4. British Sugar Beet Review, 1976. Good Beet Harvesting. 44(3):30-36. Cole, D. F. , 1976. Sugar beet physiology. Agricultural Research Service, U. S. Department of Agriculture and Department of Agro- nomy, North Dakota State University, Fargo, North Dakota, pp. 69-78. Dilley, D. R., R. Wood and P. Brimhall, 1968. Respiration of sugar beets following harvest in relation to temperature, mechanical injury and selected chemical treatment . Michigan Agricultural Experiment Station Journal , Article No. 4406 . Droll, R. W. , et a1. , 1976. Mechanical onion top removal and related pre-harvest practices. Trans. of ASAE. , 19(6):1048—1050. Finney, Jr., E. E. and D. R. Massie, 1975. Instrmentation for testing the response of fruits to mechanical impact . Trans. of ASAE 18(6):1l84—1187. Fluck, R. C. and E. M. Ahmed, 1973. Impact testing of fruits and vegetables. Trans. of ASAE, 16(4):660-666. Fort, C. A. and M. Stout, 1944. Comparative composition of different parts of sugar beet roots. Agricultural Chemical Research Division Contribution No. 225, United States Department of Agriculture. 84 13. 14 . 15. 16. 17. 18. 19. 20. 21. 22. 23. 25. 26. 85 Francia E. , 1975. Mechanical topping and sugar losses. Interna- tional Sugar Journal, 27(914):52-53. Goldsmith, W. , 1960. ’ Impact. Edward Arnold Publishers, Ltd. , london, England. 379 p. Holman, J. P., 1971.‘ Experimental Methods for Engineers. 2nd. Ed., MoGraw—Hill Book Company, New York. E3 p. Horsfield, B. C., R. B. Fridley and L. L. Claypool, 1972. Application of theory of elasticity to the desigl of fruit harvesting and handling equipment for minimum bruising. Trans. of ASAE., 15(4):746-750. Hughes, H. and L. J. Segerlind, 1972. A rapid mechanical method for determining Poisson 's ratio in biological materials. ASAE Paper No. 72-310. Jindal, V. K. and N. N. Mohsenin, 1976. Analysis of a simple pendulum impacting device for determining dynamic strength of selected food materials. Trans. of ASAE., 19(4):766-770. Kanafojski, Cz and T. Karmwski, 1972. Agricultural‘Machines, Theory and Construction, Vol . 2, Published by PWRiL, Warsaw, Poland. 1047 p. Mason, J. R. , 1952. The mechanical harvesting of beets and tops in great western territories- Proceedings of A.S.S.T. (American Society of Sugar Beet Technologists). Merva, G. E . , 1975 . Physioengineering Principles . The AVI PubliShing Company, Inc. , Connecticut, 353 p. Mohsenin, N. N. , 1970. Physical Properties of Plant and Animal Materials, Vol. I. , Gordon and Beach Science Publishers, New York. 734 p. . thsenin, N. N. and H. Goehlich, 1962. Technics for determination of mechanical properties of fruits and vegetables as related to design and development of harvesting and processing machinery. Journal of Agricultural Engineering Research. 7 (4):300-315. Neter, J. and W. Wasserman, 1974. Applied Linear Statistical 'MOdels. Richard D. Irwin, Inc., Iondon. 842 p. O'Dogherty, M. J., J. A. Wayman and F. W. Joice, 1976. Field trials with lightweight sugar beet toppers. Proceedings of International Institute for Sugar Beet Research (I.I.R.B.), 40th Winter Congress . Srivastava, A. K., F. L. Hercem and K. K. Stevens, 1976. Impact parameters related to physical damage to corn kernel . Trans . of ASAE. l9(6):ll47-1151. 27. 28. 29. 31. 32. Strooker, E. , 1969. Sugar beet harvesting mechanization in Europe and North America. (I.I.R.B.), 3(4). Tanner, J. , 1973. Economic significance and some possible approaches to reducing storage losses. Proceedings of the Beet Sugar Development Foundation Conference held in California, pp. 5-6. Timoshenko, S. P. and J. M. Core, 1972. Me'chanics of Materials. D. Van Nostrand Company, New York. 552 p. Vosper, F. C., L. F. Backer and S. Bichscel, 1976. Deep freezing piled sugar beets with forced air ventilation at Moorhead. North Dakota State University. pp. 154-160. Wyse, R. E. , 1973. General postharvest physiology of sugar beet root. Proceedings of the Beet Sugar Development Foundation Conference held in California. pp. 47—60. Zielke, R. C. , 1970. Yield and selected chemical constituents of the sugar beet root and crown. Unpublished thesis, Department of Crop and Soil Sciences, Michigan State University, East Lansing, Michigan. : IIIIIIIIIIIIIIIIIIII