A THEORY OF CORN SHELLING BASED ON ‘ A QUASl-STATIC ANALYSIS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY RUSSELL M. HALYK ‘ 1968 ‘ ’5‘, ‘2" Michigan State University This is to certify that the thesis entitled A THEORY OF CORN SHELLING BASED ON A QUASI—STATIC ANALYSIS presented by Russell M. Halyk has been accepted towards fulfillment of the requirements for M degree in Jan—Eng o fiASW: Major professor Date '[q ”01/. (98 0-169 ABSTRACT A THEORY OF CORN SHELLING BASED ON A QUASI-STATIC ANALYSIS by Russell M. Halyk An ear of corn represents an interesting geometrical structure. This structure, with its unique components, must.be dealt with each time an ear of corn is shelled. The objective of this study was to examine the geom- etry of an intact ear of corn in order to establish its relationship to the problem of shelling. The general case of shelling through the application of radial compressive loading on the ear was examined. A theory of shelling that describes the process at quasi-static loading rates was arrived at by reducing the problem to the generalized plane stress case. This theory was developed on the basis of the following assumptions: (1) that the shape of a corn kernel can be approxi— mated as that of an ordinary truncated wedge, (2) that the material constituting the kernel and cob can be considered rigid,.and (3) that the kernels are attached to.the cobs by viscoelastic connectors having properties in Russell M. Halyk tension that are different from their proper- ties in compression. Laboratory experiments at quasi-static loading rates in- dicated that the theory does predict the form of the force displacement curve of the loaded kernel. In addition, it is convenient for predicting the point in an ear where shelling is likely to occur due to the application of radial compressive loading. An attempt was made to examine the possibility of extending the theory into the dynamic range. Low velocity impact tests indicated that the energy required to induce shelling dynamically was in agreement with quasi-static test results. Significant advances in the knowledge of the material properties of a corn ear are required for a comprehensive extension of this theory into the dynamic range. These properties will have to be applicable to the high loading rates normally encountered in field shelling Operations. Approved Major Professor Department Chairman A THEORY OF CORN SHELLING BASED ON A QUASI-STATIC ANALYSIS By Russell M. Halyk A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1968 ACKNOWLEDGMENTS The author wishes to express his sincere gratitude to Dr. B. A. Stout (Agricultural Engineering) in appreciation of the continual encouragement and support that were offered during the course of this investigation. The generous assistance and constructive criticism during the preparation of this thesis were concrete evidence of Dr. Stout's unwav- ering interest in the subject; an attitude that did much towards making this a very stimulating educational exper- ience. The assistance of Dr. G. E. Mase (Metallurgy, Mechanics and Materials Science) was essential to the progress of this study, and for this assistance the author is most grateful. Thanks are due Dr. E. C. Rossman (Crop Science) for his guidance to the literature and for providing the materials used in this study. The discussions with Professor McColly (Agricultural Engineering) served to keep the main reason for this study well in mind° Special thanks are due the people of Michigan who have provided the excellent research facilities and financial assistance that have made this study possible. ii To Those teachers and friends that have provided the inspiration and encourage- ment so necessary for attempting a study of this kind. iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . . ii DEDICATION . . . . . . . . . . . . . . . iii LIST OF TABLES . . . . . . . . . . . . . . Vi LIST OF FIGURES . . . . . . . . . . . . . Vii LIST OF APPENDICES . . . . . . . . . . . . ix Chapter 1. INTRODUCTION . . . . . . . . . . . . l 2. A STUDY OF THE CORN EAR . . . . . . . . 3 2.1 Physical Description of the Corn Ear and Kernel Arrangements . . . 3 2.2 Structural Composition of the Corn Cob . A 2.3 Structure of the Mature Corn Kernel . . 7 3. THE SHELLING PROCESS . . . . . . . . . 9 3.1 Pedicel Fracture . . . . . . . . 9 3.2 Contemporary Shelling Mechanisms . . . 12 3.3 Shelling Forces . . . . . . l3 3.“ Alternate Solutions to the Shelling Problem . . . . . l5 3.5 The Need for a Shelling Theory . . . 15 A. OBJECTIVES OF THIS STUDY . . . . . . . . l7 5. DEVELOPMENT OF A THEORY OF SHELLING . . . . 2O 5 1 Simplifying Assumptions Regarding the Geometry of a Corn Ear . . . 20 5. 2- -a Kernel Geometry and Reduction 01 the Problem to the Plane Case . . 25 5.2-b Role of the Cob Structure in Shelling . . . . . . . 25 5.2-0 Modeling of the Kernel Attachment Structure . . . . . . . . 29 5.2-d Summary of the Structural and Material Assumptions . . . . . 31 iv Chapter Page 5.3-a Assumptions Regarding Applied Shelling Forces . . . . . . . 32 5.3—b Radial Compressive Loading of Rigid Model: Mixed Loading Condition . 38 5.3-0 Cases of Interest Related to Shelling in Loaded Rigid Model . . . . . AA 6. VALIDITY OF THE THEORY . . . . . . . . 53 6.1 Moisture Content Range for Which the Quasi-Static Theory Holds . . . 59 7. SHORTCOMINGS OF THE THEORY . . . . . . . 62 7.1 Rigid Material Assumptions . . . . 62 7.2 Assumptions Regarding Compressive Behavior of the Cupule . . . . 63 7.3 Ear Looseness Concept . . . . . . 63 8. EXTENSION OF THE THEORY INTO THE DYNAMIC RANGE O O C O O O C O O O O O O 65 8.1 Low Speed Impact Test . . . . 65 8.2 High Speed Moving Picture Study . . 66 REFERENCES 0 O 0 O O O O 0 0 0 0 O O O 0 7O APPENDICES . . . . . . . . . . . . . . . 76 Table A2.1 A3.l Au.l A5.l LIST OF TABLES Analysis of force-elongation curves for pedicel in tension . ., Summary of data from radial compressive tests (quasi—static loading rates) Summary of data from low speed impact tests . . . . . . Summary of regression equations describing kernel thickness as a function of its position along the ear . vi Page 86 . 89 . 92 . 97 3.1 5.1 5.6 5.7 5.8 5.9 5.10 5.11 LIST OF FIGURES Corn ears used in this study . . . . . Partial sections of a corn ear . . . . Cross-section of a corn kernel attached to 00b 0 I O O O O O O O O I 0 Corn kernels detached from cob . . . . Idealized concept of corn ear divided into periods . . . . . . . .- . . . Steps taken in reducing the problem to the plane Case 0 o o ‘ o o o o o o 0 Support structure of a corn kernel . . . Combined tension-compression elastic models Resolution of general shelling forces into two components . . . . .- . . Generalized radial loading of a corn ear in cross-section . . . . . . . . . Range of general radial compressive loading conditions . . . . ., . . . .7 . Effect of kernel length variations on force distribution in radial compressive loading 0 O O I O I O O O O 0 Initial reaction of corn ear to radial compressive loading . . . .3 . . . Cross-section of corn ear showing extension of cupules into cob . . . . . .» . Plane model of corn ear with modification to include compressive elements . . . . vii Page 10 24 26 28 30 33 35 36 37 39 Al “2 Figure Page 5.12 Loaded model with 4.5 clearance angles taken up . . . . . . . . . . . 46 5.13 Free body consideration of loaded model . . A9 5.14 Additional free body force considerations . 51 6.1 Indenter for applying radial compressive load 0 O O O O C I O O O O O O ‘5’4 6.2 Application of radial compressive load to ear of corn . . . . . . . . . . 57 6.3 A typical force-displacement curve from the radial compressive tests . . . . . . 58 6.“ Effect of ear looseness on radial compressive force required to initiate shelling . . 60 8.1 Falling weight test apparatus . . . .. . 67 8.2 Result of a drop test . . . . . . . . 67 8.3 Sequence of moving pictures taken inside a combine cylinder . . . . . . . . . 68 A2.l Experimental determination of tensile force- elongation characteristics of pedicels . 8“ viii LIST OF APPENDICES Appendix Page I. LITERATURE SURVEY . . . . . . . . . 77 A. Survey Procedure . . . . . 78 B. Periodicals Reviewed (General) . . . . 79 C. Periodicals Reviewed (U. S. D. A. and Agricultural Experiment Station Literature) . . . 79 D. Abstracts, Indexes and Bibliographies . 81. II. TENSION EXPERIMENTS . . . . . . . . . 82 III. RADIAL COMPRESSIVE LOADING OF CORN EARS: EXPERIMENTAL RESULTS AND ANALYSIS . . . 87 IV. LOW SPEED IMPACT TEST RESULTS . . . . . 90 V. EXPERIMENTS TO DETERMINE VALIDITY OF HYPOTHESIS THAT KERNEL THICKNESS IS A FUNCTION OF ITS POSITION ALONG THE LONGI- TUDINAL AXIS OF THE CORN EAR . . . . . 93 A. MOdel O O O C O O O O O O O O 9LJ B. Procedure for Obtaining Data . . . . 94 C. Data Analysis . . . . . . . . . 95 D. Results of the Analysis . . . . . . 95 VI. GLOSSARY . . . . . . . . . . . . 98 ix I. INTRODUCTION Corn ranks with wheat and rice as one of the world's leading grain crops. In a summary of agricultural produc- tion, Guidry (196”) reported that approximately 7 billion bushels of grain corn are produced in the world each year. Just over one—half of that total was produced in the United States. More recent figures by the Crop Reporting Board of the United States Department of Agriculture (1967), summa- rized the 1967 U.S.A. production as 4.7 billion bushels of grain corn. Many sources of loss are associated with the produc— tion of corn. The losses due to mechanical harvesting have been estimated by the U.S.D.A. (1965) to reduce total pro- duction in the U.S.A.~by 8 per cent. Shelling of corn appears as a comparatively efficient process, with losses estimated between 1 and 2 per cent under ideal harvest conditions (Johnson and Lamp, 1966). During unfavorable harvest conditions these losses increase well beyond 5 per cent. If average annual losses due to shelling were only 1 per cent, this means that the benefits to be derived from over 70 million bushels of grain corn could never be realized each year because of inefficiencies in the shelling process. In addition to a reduction in loss of product, improvements in harvest machine design are characterized by other factors. These include improved quality of the product, reduced equipment costs, lower power requirements and improved durability and safety. Ordinarily, improvements in the design of harvesting machines are accompanied by advances in the economics of production. Economic advancement of the producer can be a worthy goal for any study such as this. The impending world food problem, as noted by Borgstrom (1967), demands remedial action. A reduction of harvest losses through improvements in agricultural machine design can contribute significantly to a solution of this problem. Improvements in harvest machine design depend upon a clear understanding of the process and the behavior of the product under the influence of the machine system. The task that remains is clear. 2. A STUDY OF THE CORN EAR The intricate structure of a corn ear has captured the interest of many observers including artists, botanists, and anthropologists. Despite this wide interest, the form of a corn ear has been inaccurately described in many written accounts, sketches and carvings. 2.1 Physical Description of the Corn Ear and Kernel Arrangements Finan (1950) has reviewed the descriptions of corn plants which have appeared in herbals published since the third voyage of Columbus. Many other descriptions of the corn ear appear in the modern literature. The descriptions by Weatherwax (1923, 1935) seemed most appropriate to this study and are as follows: Ears range in length from 1 inch in some of the South American pop varieties, to 20 inches in some of the more vigorous flints and dents. The absence of any consistent correlation between length and diameter makes possible a multitude of shapes. There is a natural tendency for the ear to taper gradually from the base to the tip, due to a progressive decrease in the size of the cob and the grains, to closer crowding or to the loss of two or more rows. (Weatherwax, 1923) In cylindrical sections the pairs of spikelets are arranged not only in linear rows but also in certain lateral relationships which never seem to have been considered. For instance, the members of one row are not opposite the members of adjacent rows but, alternate with them. Thus if we count upward from the base of the ear and mark the tenth pair of spikelets in each row, the marked members form an undulating row around the axis, no member being out of line more than half the distance between two consecutive members of the linear row, and this is as true of the thirtieth or fiftieth pairs in the rows as it is of the tenth. In ears in which the pairs of spikelets are in an odd number of rows, that is, in ears with 10, lu, 18, etc. rows of grains, exact evenly spaced alternation is of course, mathematically impos- sible, but the undulating row around the cob is maintained. (Weatherwax, 1935) The apparent accuracy of the descriptions by Weatherwax can be readily verified by examining either an actual ear of corn or photographs (Figure 2.1) of corn ears 0 2.2 Structural Composition of the Corn Cob The cob consists of the composite structures that remain after the kernels have been removed from an ear. According to Sehgal and Brown (1965), the structure of the cob can be divided into the four arbitrary parts (Figure 2.2): 1) fine chaff--lemmas, paleas, and upper portions of first and second glumes. 2) coarse chaff--basa1 portions of first and second glumes, rachillae base and glume cushions. 3) woody ring or midcob--the rachis, nodes and internodes, inner and outer vascular system. A) pith--the soft spongy parenchymous tissue in the center. p . ,x l ‘ . I ‘ C' ‘ p.31 ‘ l‘,(('l' ' fY‘vf -f¢'1 r . ' {t‘ , - o ‘ .‘Tlf‘DI8’3? +g¢ N.‘fi((‘ .vv' ‘ 1‘7}, ' -\, L vu+ 0. L‘ AW fini’k'. 1‘.i t 1 4i L‘AL‘A'Ir' T 11111 x u Figure 2.l.-—Corn ears used in this study were of the single—cross hybrid variety 402-2X. The top ear con— tained 14 rows of kernels, the lower one 16 rows. (Photo 67—56) .pcmfin pm we 9mm mo QHB .pmoa so omonp cmanLoHHmEm who; ACOHpoomecoa :fiv mHoCLox mo pcwfip on moezaw was» opoz .boo mucoco Eoo Hmnzposppm LOnmE onp wcflzmfipcopfl new Shoo m mo mcofipoom Hmflppmmll.m.m onswam «aged 96 3583 5F. was no \ 1 [>42 88:2 383 2.3 Structure of the Mature Corn Kernel Microscopic studies of mature corn kernels have been made by several researchers. The detailed studies by Kiesselbach (1949) and by Wolf 22 a1. (1952) were most appropriate to this study because of their reference to the pedicel" (Figure 2 . 3). The shelling process implies a Consideration of the pedicel; that part which connects a kernel to its cob. Kiesselbach (1949) stated that "upon shelling the flower stalk or pedicel commonly remains attached to the base of the kernel." Wolf 32 a1. (1952) noted that: . . . usually the kernel separates from the cob at the base of the tip cap. Sometimes, however, the tip cap remains attached to the cob and is removed by subsequent handling of the kernel. When present on the kernel, the tip cap is easily removed by a slight pull, exposing the dark hilar layer which lies above it and covers the base of the kernel. *See Glossary, Appendix VI e ‘§ a' i , .7: ‘.§ v I \un Figure 2.3.4—Cross—section (r a -. ‘,.. . .‘ill attached to the cob. Actual width.cf H'b’4 ‘ - “~ ea: 0.32 inch. Approximate magnification = 9... ' ' ‘ . '"170—2) qua qi'l' (leoibo‘l) to nwowO lame)! l .! ‘1». Figure 2.3.--Cross-section of a corn kernel still attached to the cob. Actual width of kernel at center was 0.32 inch Approximate magnification = 9.2. (Photo No. 68370—2) "n 134 --'l 3. THE SHELLING PROCESS Shelling of corn is defined as the process of detaching corn kernels from their cobs. The process entails frac- turing of pedicel tissue. Usually, fracture occurs at the tip cap (Figure 2.3). Miles.(l956) noted that when kernels have been removed at a high moisture content then a portion of the kernel tips breaks off and remains with the cobs (Figure 3.1). Kiesselbach and Walker (1952) reported that when moisture content of the kernels is reduced to approxi- mately 34 per cent and that of the cob to about 53 per cent, then physiological maturity is attained. At that point the moisture and nutritional connection between the kernel and the cob has become severed by suberization of the tissue at the base of the kernel. The suberization process may determine whether the tip cap remains attached or breaks away. 3.1 Pedicel Fracture Hall (1961) has determined that the amount of force required to fracture a pedicel in pure tension depends upon the moisture content of the kernel. He found that average force required to detach a kernel from its cob ranged between 1682 grams (3.71 pounds) and 2555 grams (5.63 pounds). Rate of load application was not reported. 10 Figure 3.l.—-Detached corn kernels. Kernel at right had tip cap missing due to shelling at a high moisture content. (Photo 68370-6) ll Waelti and Buchele (1967) reported that the kernels of some varieties required greater tensile forces for detaching them from their cobs than did the kernels of other varieties. Rate of load application was variable. The effect of variety on ease of shelling was recognized as early as 1624 A.D., though not in a quantitative way. Weatherwax (1954) stated: Many of the flinty varieties had smooth, rounded grains which were very firmly attached to the cob. These were often shelled by rubbing the ears together or by rubbing them over a rough stone or similar object. At the other extreme there were some varieties especially in South America, whose grains were attached so loosely that most of them could be removed simply by shaking the ears in a basket. The force required to detach a kernel of corn grain from its cob in pure tension does not appear to be affected by its position on the cob. From the data gathered by Waelti and Buchele (1967), differences in the force required to remove kernels from either the tip, middle, or basal regions of an ear within a given variety were not signifi- cant. The rate at which load is applied to a kernel of corn in order to cause fracture of the pedicel is an important variable. Zoerb (1958) found that corn kernels exhibited a viscoelastic behavior. Mohsenin (1966) indicated that there is experimental evidence that most agricultural products are viscoelastic. The viscoelastic property implies a sensitivity to rate of loading. 12 3.2 ContemporaryiShelling Mechanisms One of the ultimate objectives in the design of an effective shelling device is the capability to remove all of the kernels from an ear of corn without incurring damage to either the kernels or the cob. Two types of field shelling mechanisms have been developed out of the many attempts at this objective. The two shelling mechanisms found on American farms today are the cage-type sheller and the cylinder-type sheller. Johnson and Lamp (1966) have reported that both are capable of high shelling efficiencies when moisture content of the corn is low. However, when the moisture content of the corn exceeds 20 per cent, or when moisture of the cob exceeds 25 per cent, Goss 33 31. (1955) and Burrough and Harbage (1953) found that the performance of these mechanisms degenerates. The immediate result is that losses are sustained both in the quantity of grain obtained and in the quality of the resulting product. The losses that are sustained through the operation of these shelling mechanisms appear to be unavoidable. Extensive studies by Byg 33 31. (1966) in Ohio reported that average seasonal losses from combined picking and shelling machines ranged from 1.6 to 4.0 bushels per acre more than the losses incurred by picking ear corn. Similar results were obtained by Goss 33 31. (1955) in California. 13 The consistency with which shelling losses are reported indicates that they may be inherent in the action of these mechanisms. In order that the real effectiveness of these mechanisms may be determined, it is necessary to know the kinds of forces that they impose on an ear of corn during the shelling process. 3.3 Shelling Forces The kinds and magnitudes of forces that are imposed on an ear of corn when it is being shelled in either a cage- type or cylinder-type sheller have not yet been clearly defined. Johnson and Lamp (1966) have reviewed the recent literature pertinent to the shelling actions of these two mechanisms. They reported: The cage-type sheller consists of a cylinder with lugs, spiral flutes, or paddles which turn inside a cage. The cage hasa perforated surface with holes large enough to let the kernels fall through but retains the cobs. The ears are fed, normally from two rows, into an Opening at one end of the cage. The spiral flutes feed them through the cage and at the same time shell the ears by a rolling and crushing action against the cage surface and against each other. The cylinder type of sheller is used in combines. The corn is shelled by the impact of bars placed axially on the periphery of the cylinder as the corn is crushed against the concave. ... ~The intensity and number of blows received by an ear of corn as it passes between the cylinder and concave depends upon cylinder speed and resis- tance on the concave as determined by the number of concave bars and cylinder-concave clearance. 14 High speed photography can be an effective tool in qualitatively determining the kinds of forces that are imposed on an ear Of corn while it is being shelled. A high speed moving picture camera was used by Hopkins and Pickard (1953) in order to analyze the action within a combine cylinder during shelling. Their studies were r—— designed to determine the magnitudes of the forces that exist between the concave and the cylinder during the shelling process and were not primarily concerned with the analysis of forces on the individual ears of corn. A lack of information on shelling of corn by impact ' still exists despite the fact that the process has a pre- Columbian history. Weatherwax (1954) noted that the prim- itive Indians of Western Mexico shelled corn by placing the ears in coarse bags, suspending the bags like hammocks and beating the bags with contents by means of suitable clubs. The shelled grain could fall out through the Openings in the coarse mesh. Rubbing forces have also been used by these primitive Indians in order to shell corn. The ears were usually rubbed against a rough surface formed Of corncobs. This action may be similar to that of the "rolling and crushing" which takes place in a cage—type sheller. The foregoing descriptions of the shelling process indicate that some combination of radial-compressive and tangential forces is engaged to produce the desired results. 15 A theory of shelling can therefore justifiably assume that these are the forces which cause shelling to occur. On- the basis of this assumption, the entire range of possi- bilities which can exist must be satisfied by one of the following: 1) shelling by combined tangential and radial- compressive loading. 2) shelling due to pure radial compressive loading. 3) shelling due to pure tangential loading. 3.4 Alternate Solutions to the Shelling ProBlem Shelling of corn can be achieved in various other ways besides the application of impact and crushing forces. Jain (1966) has shown that when the cob is subjected to axial loads, shelling occurs. Lamp (1959) performed experiments demonstrating that centrifugal forces can also be used effectively to achieve shelling. 3.5 The Need for a Shelling Theory The lack of a clear understanding of the shelling process becomes apparent from the vague descriptions re- quired to characterize shelling forces. Terms such as "crushing" and "impact" are insufficient for accurate de- scription of a problem. Consequently, present insights into the shelling processtunmaadvanced very little beyond those of the Columbian Mexican Indians Observing their colleagues at the manual task of shelling corn. 16 The recent interest of agricultural engineering researchers in such fundamental properties as the attach- ment strength of kernels to cobs can be considered as substantial evidence of a search for a better understanding of the shelling phenomenon. Successes in other fields, such as engineering mechanics, indicate that the formula- tion of reliable theories from such studies can do much towards the advancement of knowledge in a subject area. Analogously, the development of a theory of shelling can serve to advance understanding of the shelling process. 4. OBJECTIVES OF THIS STUDY The general objective of this study was to attempt an integration of present knowledge about the shelling process with the information available on the properties of corn ears into a unified theory of shelling. Such a theory could prove useful in analyzing those harvest machines that induce shelling by subjecting corn ears to radial compressive and tangential loading. Formulation of an exact theory of shelling that would describe the actual phenomenon implies a dynamic analysis of the problem. Furthermore, such a formulation requires consideration of the dynamic mechanical properties of the material. An extensive literature survey (Appendix I) failed to disclose information of this nature which would correspond to loading rates ordinarily associated with the shelling process. The heterogeneous nature of the material, complicated structure of the ear and vague descriptions of the shelling process suggested the desirability of developing such a theory through a stepwise procedure. .The formulation of a rigorous quasi-static theory could serve as the very impor- tant first step in this development. 17 l8 Ordinarily, the application of static test results to a dynamic phenomenon is considered no better than an extrap- olation of the facts. Eirich, in the introduction to the proceedings of the first symposium on high speed testing (Dietz and Eirich, 1960) stated: I This is an age of high speed in everything except testing of materials. This is particularly true- in fundamental as Opposed to engineering testing and leads to the paradoxical situation that much of material behavior during actual performance has to be extrapolated from laboratory tests at much lower speeds. There are, of course, good reasons for this situation, the principal one being that the exact conditions during actual performance are often unknown or very difficult to duplicate. There is also another, more basic cause. All studies of mechanical behavior require the correlation of stresses with strains and/or strain rates ob- tained from deformation experiments of rather simple geometry and with clearly defined vari- . ables. The measurement at high speeds of stresses and strains demands electronic or Optical equip- ment of high complexity. Furthermore, very few materials develop large strains at high speeds before they fail. Failure, in general, is always due to the growth of existing cracks and flaws in the test piece and is therefore statistical in nature and depends on the specimen size. Eirich, of course, was referring to materials much more amenable to materials testing procedures than most agricultural products usually are. In view of the antici- pated difficulties associated with a dynamic analysis of shelling, the Objectives of this study were directed towards approaching the problem from a quasi-static viewpoint. 19 The specific objective of this study was to formulate a suitable quasi-static theory of shelling for a general case. The theory would be developed around laboratory studies designed to Observe the behavior of corn ears under loads similar to those normally encountered in field shelling mechanisms. The suitability of the theory would be assessed by the accuracy with which it predicts the behavior of actual corn ears. The possibility of extending the theory into the dynamic range was considered also. Such considerations were restricted to qualitative Observations of the dynamic process. The observations could also serve as the prelim- inary investigations for a detailed study of the dynamic behavior of corn ears during shelling. Such a study has been planned as part of a continuing program at Michigan State University with the ultimate objective of developing a comprehensive dynamic theory of shelling. 5. DEVELOPMENT OF A THEORY OF SHELLING The nature of the shelling problem suggests that simplifying assumptions be adopted in the development of a theory. Such assumptions are necessary because of the many interrelated factors entering the problem. Various approaches can be taken in the develOpment of a suitable theory. An effective approach can be one which begins by assuming the simplest conceivable model of the problem. Development proceeds from that point by phasing out the crude assumptions either by modification or replacement. In this way it is possible to arrive at a theory that is applicable to typical ears of corn within acceptable error limits. This procedure is consistent with Toulmin's (1961) outline on evaluating the merits of a theory and its potential as a contribution to the evalua- tion of scientific ideas. 5.1 Simplifying Assgmptions Regarding the Geometry of a Corn Ear The descriptions of a corn ear by Weatherwax (1923, 1935) point to the existence of a repetitive pattern in-the arrangement of kernels in an ear. Although these patterns Imiy be repetitive, there exist important variations of parameters within them. For instance, kernel dimensions become smaller near the tip of the ear. 2O 21 Ancillary eXperiments were conducted to assess the applicability of this concept of description. Kernel thick- ness, that dimension of a kernel which is parallel to the longitudinal axis of a corn ear, was measured for all of the kernels from several rows of different corn ears. A statis- tical analysis of the results was made, using the simple model: t = _§_. (5.1) 1 1+1 where, ti = thickness Of any kernel 1. i = period under consideration in the sequence 1, 2, 3, . . . The sequence was started at the basal end of the ear. A = a constant I = an integer constant. The equation (5.1) could be further simplified to: if it is understood that any particular sequence does not necessarily begin with the period numbered one. A high correlation between the theoretically predicted and actual dimensions for some ears indicated that such math- ematical modeling can provide an adequate solution to the problem of simple mathematical description (Appendix V). The Weierstrass Approximation Theorem (Tolstov, 1965), of course, 22 proves that a polynomial exists which will describe such a parameter as accurately as desired. However, that polynomial may be of such a complicated form that it no longer serves as a practical form of description. A similar approach was reported by Frey-Wyssling (1957) and by Esau (1966) for describing the helical arrangement of leaves and buds along a shoot. The Fibonacci sequence 11235 8 23581—35 LOH LA) was used. Development Of the surface of a corn ear can also serve as an effective tool in elucidating ear geometry. If the concept of a repetitive pattern is superimposed on the development technique, the resulting figures can lead to further insights into the arrangements of kernels in an ear of corn. Consider an ear of corn having negligible taper. Development of the surface becomes equivalent to the develop- ment Of a cylinder. If the length of the cylinder is divided into shorter sections which can be called periods, (Figure 5.1) then the concept of a sequence emerges. And if more than one parameter is considered, say kernel length, thickness, weight and cob diameter, then a sequence of func- tions is generated. These in turn can yield one or more series of functions, thus providing additional information about the ear. For example, the summation of kernel thick- ness results in ear length data, as in the equations: 23 n n A Length = 1:1 ti = 1:1 ITI where, ti = thickness of any kernel i i = period under consideration in the sequence 1, 2, 3, . . . A = a constant I = an integer constant n = total number Of periods in the ear. A single period within a sequence can be defined in several ways. A11 definitions are acceptable provided that they retain the recurrence of geometrically similar forms. In the present case, cylindrical sections of two kernel thicknesses were considered as one period. This was done in order to minimize variation of any particular parameter within a period, and was based on the assumption that kernel dimensions vary only according to their position along the longitudinal axis of the corn ear. Variation Of any parameter within a particular period cannot be entirely eliminated so long as that parameter is affected by its position along the length of the ear. This holds even if periods of one kernel thickness are considered, because Of their alternating arrangement. The consideration of periods consisting of more than two kernel thicknesses should therefore be avoided. 24 . .Oouooaom Ohms OOH: mommocxcfinp Hocsox 03» mOOfipoa oaasmxo was» CH .Eouuon .vOfipoa oco an OOCHMucoo oomMASm on» mo ucoeaoao>oa .OOO .mnoapoa Opzfi OOOH>HU mam shoe a no pmoonoo OONHHmOOHII.H.m mnswam t m. n. e. m. u. : o. m m s o m e n N . ul-..i.l 4 out“: I» _ v: Jul.» _ on I_ II !. iUK _ NILE...“ _ NIL... A L e 25 The development of a period consisting of two kernel thicknesses is shown in Figure 5.1. It can be seen, by attempting to reconstruct the cylindrical surface from this development, that row number 1 will only match properly with the kernels in even-row (8, l2, l6, . . . that is, exactly divisible by.4) ears. Misalignment occurs when Odd-rows (10, 14, 18, 22, . . . ) are considered. This mis— alignment sometimes results in the twisting of actual corn ears, as shown in Figure 2.1. 5.2a Kernel Geometry and Reduction of the Problem to the Plane Case The preceding descriptions and development indicate that the shape of an individual kernel approaches that of a truncated pentagonal wedge. If the shape is assumed to be that of an ordinary truncated wedge instead, then visual- ization of traction forces on an ear of corn can be more easily realized. Indeed, plane case generalizations can then be introduced as desired in order to analyze the action of forces on this geometrical structure. These simplifica- tions are outlined in the drawings of Figure 5.2. 5.2b Role of the Cob Structure in Shelling The shape of a corn cob closely resembles a truncated cone. Jain (1966) considered the corn cob as a hollow elastic cylinder. The hollowness assumption appears valid for that .mmmo Osman one Op annona on» mo COHp03OOL CH wQOme|.m.m opsmflm 2250:3570. meow; 53.83 L 26 um . Elastic Tension or Compression Mode! W I Integrated Model-Units Independent «estate 1,, Integrated Model-Units lnterrelated Integrated Model-Units Interrelated Figure 5.4.—-Combined tension-compression elastic models adapted to the case where tensile behavior differs from the compressive reaction. The technique can be extended to include viscous elements. Dependence refers to the compressive reaction. 31 but require removal of adjacent tissue which may entail disturbance of the results. Inialternate approach is to assume that the material constituting the cob and kernels is hard, and therefore does not deform significantly. A rigid material assumption for the kernel and cob requires justification. Ancillary eXperiments were con- ducted to determine the validity of such rigid material assumptions. Fromtflm’available literature and experimental results (Appendix II) it was found that this assumption leads to errors less than 4 per cent in the 11 per cent wb to 19 per cent wb moisture content range. 5.2d Summary of the Structural and Material Assumptions The foregoing discussion on simplifying assumptions has pointed to the desirability Of assuming an ear of corn to consist of rigid kernels and a rigid cob. The connections between the kernels and the cob can be visualized as visco- elastic links whose properties can be determined experimen- tally. Examination of an ear of corn indicates that spaces exist between kernels. These spaces seem to be larger in some ears than in others. Observation of this fact plus a recapit- ulation of elements frOm the previous discussion in this chapter leads to the plane case generalization of Figure 5.6., This model differs from the plane case of Figure 5.2 in that clearances between the kernels have been introduced. 32 Clearance between kernels has been assumed to be angular (Figure 5.9). A detailed analysis may prove that clearance is the same at both the inner and outer diameter of the ear. This detail is not fundamental to the study. 5.3a_ Assumptions Regarding Applied Shellinngorces The geometry of a corn ear permits a wide class of surface forces to serve as potentially admissible shelling forces. Those surface forces which will be considered in- admissible as shelling forces in this study are of two kinds, namely: 1) Forces acting on the inside surface of the cob due to the hollow cob assumption of section 5.2b. 2) Forces acting on either one or both ends of the cob so as to produce axial shelling similar to that reported by Jain (1966). Every surface force acting on an ear of corn can be completely specified by three force components, regardless of the coordinate system considered. The cylindrical co- ordinate system aids in visualizing all admissible shelling forces as a combination of only two components: one radial, the other a directed tangential component, as illustrated in Figure 5.5. A convention for measuring the angle W should consider the positional relationship Of the kernel acted upon and those it is forced to bear against. Bearing may be against either aligned or alternating kernels. .pcmEmwcwpam Hashes an coeducac cowpco>coo m on weauaooom omcfiuoo on pass a oawcw on» no acoEouSmmoz .muCOGOQEOO 03p Oped mmohom mafiaaonm Hmpocmm mo coauSHOmmmit.m.m opswam Emcee—coo .303.— Eocanoo .2235... 389.5 33 228.50 .063. \\ / 34 Radial loadings of homogeneous and composite cylinders usually appear as problems in diametral compression. This kind of loading can also apply to a particular case in the shelling of corn. A generalized case of shelling due to the application of radial compressive loading is illustrated in Figures 5.6 and 5.7.- Here the load P is resisted by the two components yP and (l-y)P. The factor y simply describes the fraction of the total force that is transmitted to the kernel in the same plane and diametrally opposite the point of load appli— cation. For radial compression, O> ktensile where k is the usual spring constant from the force- displacement equation: F = kx. Movement of the adjacent kernels in a circumferential direction will also occur if tangential force components are large compared to the radial forces. This is true when the coefficient Of friction between kernels is small. 41 Figure 5.10.——Cross—section of a corn ear. Cupules, which support the bases of the kernels, extend deep into the structure of the cob. (Photo 68370—5) 42 Clearance Angle ‘ ...... Rigid Cob C O + ———_—-—_ . Kernel -’ \ Compressive Element Tensile Element _ . A 7 Clearance Angle Cob Figure 5.11.--P1ane model Of the ear modified to include compressive elements. A11 kernels have identical connecting structure shown at bottom. 43 The model in Figure 5.11 consists of elastic elements only. Appropriate viscoelastic elements can be substituted directly into the model to account for the time dependent properties of the.pedicel and surrounding support structure. This procedure is in accord with the well known correspondence principle of viscoelasticity (Bland, 1960). It should be noted that the position of the compressive elements is important in describing resistance of the kernels to bending forces. The modeling approach taken by Moustafa (1966) may be useful in such a problem. .-.9" Increase in the load P causes succeeding clearances to be taken up. When j+f clearance angles are taken up, the radial displacement is given by: _ sin (j+f) Y x _ Ri sin a (5‘2) where, x = displacement of radially loaded kernel towards center of the ear. R1 = inside radius of kernels. Y = clearance angle between kernels prior to loading. j = the number of clearance angles completely taken up between the loaded kernel and the point diametrally across. n = total number of kernels in the model. 44 f = fraction Of one clearance angle taken up. a = one half the angle included by a kernel. In the above equation, must hold. 5.3c- Cases of Interest Related to Shelling in Loaded Rigid Model Loading of the model has at least two cases of interest. One case occurs when the pedicel on an adjacent kernel is elongated to the point of fracture. The second case occurs when all of the clearance angles in the model have been taken up due to circumferential movements of the kernels. Case 1: Fracture of pedicel in adjacent kernel. Elongation Of the pedicel in any kernel can be deter- mined from the geometry of the problem. The geometry is based on a previous assumption: that movement of all kernels, except the loaded one, is in a circumferential direction. Consider any displaced kernel g in the loaded model. In order that this kernel can be referred to specifically, a naming or numbering system is required. The system adopted here uses numbers. The number, one, is assigned to either of the kernels adjacent to the kernel being loaded. The following numbers are assigned by counting in the direction away from the radially loaded kernel. Thus 45 there will be two kernels with the number one, two with the number two, and so forth. End of the counting sequence occurs at or before a point diametrally Opposite the radially loaded kernel. Assume j+f clearance angles have been taken up due to the displacement of the radially loaded kernel. Then, from may. the previous discussion: sin (j+f) I x = Ri sin a The initial length of any pedicel g (Figure 5.12) is given by: L = R1 - Rc where, L = initial length of any pedicel R1 = inside radius of kernels RC = radius of cob. For the kernel g to be displaced it is necessary that After_1oad P is applied so that j+f clearance angles are taken up, the cosine law yields the following equations: L; = /[Rj2_ + F3 — 212113C cos (j+f-8W] (5.3) 0‘ 46 x ‘«i M Figure 5.12.--Rigid model loaded with j+f = 4.5 clearance angles taken up. 47 t where Lg is defined as the new length of pedicel g due to the displacement of that kernel. Elongation of the pedicel for kernel g is g g = //[R§ + RS — 213113c cos (j+f-g)Y] - L e = /[R2 + R2 - 2R R cos (j+f-g)Y] - R +R (5 4) g / i c i c i 0 ° n for. g = l, 2, o o o, '2- 1 It is evident from Figure 5.12 and from the above equation that maximum pedicel elongation occurs in the kernels adjacent to the radially loaded one, for which g = l. Elon- gation of either pedicel to the point of fracture signifies the initiation of shelling. Case 2: All Clearance Angles in the Rigid Model Completely Taken Up When the displacement, x, of the radially loaded kernels becomes R sin 27 x = i 2 (5.5) sin a and shelling has not commenced, then all of the clearance angles in the rigid model are taken up. The above statement 48 was obtained by setting j+f at its maximum value,%, in the equation (5.2). Since symmetry of the model has been assumed, then the bounds on x are given by O ;_x < Ri - R0 for radial compressive loading. Near the upper bound (Ri - Re), the compressive elements approach zero length in the model.- The distribution of forces in the model is determined largely by the behavior of the attachment structures of the kernels. A force, or stress, analysis of the problem be— comes necessary if strain in the first pedicel, g.= 1 is not sufficient to have initiated shelling at this point. The applied radial compressive force P is resisted by the compressive reaction of the loaded cupule plus the friction which results from wedging apart of the two adja- cent kernels. The problem of analyzing the forces acting on the loading kernel is statically indeterminate unless either H, the wedging force (Figure 5.13) or CO, the com- pressive resistance is known. Let it be assumed that the force—deformation behavior of the cupule structure is known. lflmniCocan be related to the displacement x of the loaded kernel. Knowing this, H can be determined if the coefficient of friction between kernels is known. Burmistrova.33 31. (1963) reported u = 0.36 for this, which corresponds to a friction angle of 19.8 degrees. 49 X ___L Figure 5.13.—-Free body consideration of the rigid model with all clearance angles taken up. H is the wedging force in the model due to the radial-inward displacement of the loaded kernel. The subscripted force vectors de- note cupule compression (C), pedicel tension (T), and frictional-compressive components (F). 50 With H obtained in the above manner, the three free- body diagrams of Figure 5.14 can be considered. These three force diagrams will yield 9 equilibrium equations, but only 6 of these equations will be independent. There are 7 unknown quantities which must be evaluated, namely: C1 = the compressive force exerted by the cupule on kernel g = 1. C2 = the compressive force exerted by the cupule on kernel g = 2. T = the tensile force exerted by the pedicel on kernel g = 1. T2 = the tensile force exerted by the pedicel on kernel g = 2. F12 = the compressive-frictional force exerted by kernel g = l on kernel g = 2. F = the compressive—frictional force exerted by 21 kernel g = 2 on kernel g = 1. F32 = the compressive frictional force exerted by kernel g a 3 on kernel g = 2. Note that F12 = -F2l, so that it is possible to solve for each of the unknown forces in terms of H. Furthermore, these can be related to the applied load P. The Figure 5.14 shows F cand F for the case where 21 12 motion is impending between kernels g = l and g =.2.~ In~ other words, the kernel g = 2 is beginning to shell. The 51 / T2 C/\ F32 2 T: F Cg 2| Figure 5.14.-—Additional free body force considerations for the case where ejection of kernel g = 2 is imminent. (1 + u2)H is abbreviated FOl 52 indeterminate condition on kernel g = 2 suggested the placing of limits on the force F32. These were determined by assuming a friction angle of 19.8 degrees and considering sliding in both directions, that is kernel g = 2 past kernel g = 3, or the reverse. Shelling is initiated when either T or T exceeds the ultimate tensile strength Of the 1 2 pedicel. 6. VALIDITY OF THE THEORY Any theory of shelling can be considered valid if it accurately predicts the response of a corn ear to the kinds of forces that were considered in the formulation. This criterion was stipulated as one of the objectives of this study. Quasi-static tests were conducted to determine the response of corn ears to radial compressive loading. Loads were applied to the crowns of individual kernels by means of a flat surfaced steel indenter. The indenter was shaped to cover the entire crown of an average corn kernel. Its size and shape (Figure 6.1) permitted a distributed loading of individual corn kernels without disturbance to the adjacent kernels. In the compressive tests, an entire corn ear was placed on the load cell platform of an Instron model TM testing machine. The Instron model TM is a constant rate of travel testing machine. Load was applied by means of the specially shaped indenter which was mOunted in the cross- head. Time dependent behavior of the pedicel and surrounding structure was anticipated. Therefore, loading rates of 0.1, 53 E/{NF Locknut o. 077" R. Figure 6.l.--Indenter that was used for applying radial compressive load to individual kernels. 55 0.1 and 1.0 inch per minute were selected to determine the effect of loading rate on the compressive behavior of the pedicel structure. Preliminary tests showed that corn ears having a high moisture content (above 15.3 per cent wet basis) would yield information of dubious value to an understanding of the shelling process. The crowns of kernels were crushed when relatively small loads were applied on them. Continuation of loading after crushing Of the crown was pointless since the information did not seem related to the shelling process. On drying to some specific moisture content it appeared that the response of a corn ear to radial compressive loading was completely changed. Application of compressive load to the crown of a kernel no longer caused crushing. Instead, a kernel in the adjacent region would be ejected from the ear (Figure 6.2). The particular kernel that would be ejected from the ear could be predicted with some accuracy. From the pattern of Figure 5.1 and the theory, either the kernel in the adjacent paired (rather than alternate) row, or one Of the two adjacent alternates in the following row (g=2) would be shelled. Shelling in the adjacent alternating row was infre- quent and was attributed to some tangential component in the loading. 56 A typical force-displacement diagram for loading an ear in radial compression is given in Figure 6.3. This reaction could have been predicted by the rigid kernel and cob theory. The initial linear portion of the curve is attributed to the constant rate reaction of the attach- ment structure in the loaded kernel. As interference from the adjacent kernels comes into play, the curve deviates from the initial straight line. The deviation continues to increase as additional clearances are taken up in the ear. : Data from the compressive tests (Appendix III) were 13 rv—VK subjected to a multiple linear regression analysis. The parameters usually associated with kernel damage in shelling were considered as independent variables that might affect the force required to initiate shelling. These parameters included moisture content of the kernel, cob moisture content, date Of harvest and rate Of loading. A low coefficient of determination for the above analysis indicated that other variables should have been in- troduced. The theory predicts that the number of rows per ear and some measure of ear looseness or clearance angle should have also been considered. The rigid material theory predicts that higher loads are required to cause shelling in a loose ear of corn than in one in which the kernels are tightly packed. This factor 57 l/.:»' . . ,..MWMW~~—o u-a_. 0W4“; .Mw'ew e-‘MWWo. .JeH“ "“ ' (.1 V . ...-wen nonuummwm Figure 6.2.——Application of radial compressive load to an ear of corn. Note the ejection of a kernel from an adjacent row. (Photo 67—17) .mpmou o>fimmmnasoo Heaven on» 809% O>LSO pCOEoomHOmHOImopom HmOfldzp <|i.m.m meswfim ..mzmmv. omo<04 m0 Fzmzwonfiama IOUJOM 00140913 30305 amssaadwoo ‘lVlOVH 59 had not been realized prior to the quasi-static compressive tests. However, ear looseness could be simulated by removing one row of kernels from an ear prior to loading. In several repeated tests it was found that much higher loads are required to cause kernel ejection in an ear after a row Of kernels has been removed from it. A typical force displacement record Of this is shown in Figure 6.4 for a particular corn ear. The first two tests were con- ducted on kernels in the same row spaced l3 kernel thick- nesses apart. The third test shows the effect on force required to cause shelling when radial compressive load was applied to a kernel after shelling was initiated in the ear. This was done by removing all of the kernels in the row g=3. Although ear looseness was artificially induced, the large difference in required shelling force suggests that ear looseness may be an important factor related to shelling. 6.1 Moisture Content Range for Which the Theory Holds The main Objective of the quasi-static experiments was to determine the moisture content at which shelling can be induced by radial compressive loading. Since moisture contents of the crop on harvesting were such that shelling could not be initiated at the quasi-static load rates, the corn ears were permitted tO dry in the laboratory atmos- phere until shelling could be achieved in this way. 60 .Lem one Eopm ow>oEmn comp we: maocpmx meow Loewe wcfiaaonm omsmo Op empaseop mopom ecu cane Lozoa zanepoewmcoo we; shoe no new cm cfi mcHHHocm mpmHuHcH Op OOLHSOOL oopom O>HmmopQEOo Hmwommtt.:.o whswfim 33... tom .3233 353. Kernel Ejection Ear lntoct memo... w>_mmwmm 200 45041 DISPLACEMENT OF LOADED KERNEL 61 The drying rate of the corn ears, which were placed on a. tabletop for drying, was such that moisture content of the ears was reduced an average 2.6 per cent per day. Laboratory temperature during the drying period fluctuated between 77°F and 81°F, with relative humidity ranging between 20 per cent and 32 per cent. The procedure of laboratory drying is not recommended, for it may lead to unnatural moisture relations between the kernel and cob. This procedure was deemed permissible here only because the quasi static loading rates were also unnatural to the shelling process. It was found that shelling can be induced at quasi- static load rates when the moisture content of the kernels is 15.3 per cent or less; that of the cobs 24.9 per cent or less. Ear moisture averages would be somewhere between these two values. 7. SHORTCOMINGS OF THE THEORY The theory developed in this study describes the reaction of a corn ear to applied radial compressive loads with a qualified accuracy. In the development, hypothetical assumptions were made to explain the Observed behavior of actual corn ears. 7.1 Rigid Material Assumptions The rigid material assumptions appear very unrealistic as a first impression. However, when considered within the context of the problem, they serve a useful and meaningful purpose by simplifying explanations considerably. The errors which they introduce are probably small. The hazards associated with these material assumptions are that they conceal many important aspects of the problem. The rigid cob and kernel theory, for instance, precludes shelling by the application Of axial load on the cob. This factor is readily apparent because Of its physical conse- quences. What may not be so readily apparent are factors such as interdependence of kernels within a row. The structure of the cupules suggests that such interrelations should exist; that kernels are interdependent. A knowledge of material properties such as Poisson's ratio and bulk modulus is important to an understanding of this inter- dependence from the materials point Of View. 62 63 7.2 Assumptions Regarding Compressive BehaVior of the Cupule The compressive behavior of the cupule was assumed to permit pure rotation of kernels about the cob center. Actual measurements of the motion induced in an ear by the application of bending loads to the kernels should be made. These motions are particularly important to a dynamic analysis of the problem. Structural models similar to those developed by Moustafa (1966) could be an important asset to understanding the stability of attachment of corn kernels to cobs. Such models would remove many of the doubts associated with ideas like sliding spring elements. More importantly, they would aid considerably in extending the theory to include shelling by the application Of tangential forces to the ear. 7.3 Ear Looseness Concept Introduction of the ear looseness concept was required in the rigid material theory. Its importance to the actual problem of shelling by the application of radial compressive loading needs to be ascertained for corn in its various harvest conditions. The need for an ear looseness concept vanishes when deformable kernels are considered. A study of ear loose— ness would then correspond to the properties of the kernel m 64 material in the directions perpendicular to the length of the kernel. The composition of corn kernels suggests that anisotropic behavior should be expected. 3:“. 1h 8. EXTENSION OF THE THEORY INTO THE DYNAMIC RANGE Corn is usually shelled at high rates of loading. Impact velocities between 2500 and 3500 feet per minute me are common in cylinder type shellers. In order that the foregoing theory may have practical 4r ."i‘l-g- .I value, it must be extendable into the dynamic range. This criterion was one of the objectives established for this : study. A dynamic analysis Of the shelling problem requires a knowledge of the dynamic mechanical properties of corn. The lack of such information suggested that a qualitative analysis of shelling by radial impact be considered. 8.1 Low Speed Impact Tests Corn ears were subjected to low speed radial com- pressive impact loading. The special indenter used in the quasi static experiments was adapted to a falling weight test apparatus (Figure 8.1). The maximum height of drop available with this apparatus was approximately 5 feet. Minimum weight that could be dropped was 1.25 pounds; max- imum weight was 12 pounds. 65 66 Using the minimum dropped weight (1.25 pounds) it was noted that shelling could be initiated from drops as low as 0.41 feet. The experiments (Appendix IV) indicated that an average 0.51 foot pounds of energy were required to initiate shelling in dry corn. The physical results of a drop test can probably be best explained with a photograph. Figure 8.2 shows the result of one drop test in which two kernels were ejected. Although the theory did not predict shelling of kernels in the same row as the load was applied, variations in kernel shape from the idealized model did allow this to occur. 8.2 High Speed Moving Picture Study High speed moving pictures that have been taken in- side the shelling mechanism Of a corn harvesting machine can provide information useful to a study of shelling. The sequence of pictures in Figure 8.3 shows the reaction of a corn ear to impact by a cylinder bar. The sequence ends with compression against a concave bar. The loading of an ear of corn that takes place within a cylinder-type sheller may be purely radial compressive by accident rather than intent. The reaction of the corn ear in the sequence of photos (Figure 8.3) was such.that kernels were ejected from the ear near the point of loading. This is in agreement with the results predicted by the quasi- static theory. 67 Figure 8.1.--Falling weight test apparatus. Weight with special indenter is shown in the dropped position. (Photo 67-58) ,, ..lll‘ Figure 8.2--Result of a drop test. In this case an 1.25 pound weight was dropped from a 0.5 foot height. Velocity at the beginning of impact was estimated to be 330 feet per minute. (Photo 67-57) «Mime/7 .32.. 2"” 1o. 68 Figure 8.3.—-Sequence of moving pictures taken inside a combine cylinder. Peripheral velocity of cylinder was 2600 feet per minute. Camera speed was 4000 frames per second. (Photo courtesy Massey Ferguson Ltd., Toronto) 69 The vagueness associated with these Observations can be dispelled by a dynamic analysis of the problem. Such an analysis should be linked with experiments in which loading can be controlled. REFERENCES Aldrich, S. R. and E. R. Leng 1965 Modern Corn Production. F and W Publishing Corp., Cincinnati. 308 pp. Anderson, E. I“ 1944 A method for recording and analyzing variations of internode pattern. Annals of the Missouri Botanical Garden 31:241-247. Bland, D. R. 1960 The Theory of Linear Viscoelasticity. Pergamon Press, New York. 125 pp. Bonnet, O. T. 1948 Ear and tassel development in maize. Annals of the Missouri Botanical Garden 35:269-288. Borgstrom, G. 1967 The Hungry Planet. The Macmillan Co., New York. 507 pp. Burmistrova, M. F. et a1. 1963 Physicomechanical Properties of Agricultural Crops. Translated from the 1956 Russian version by the Israel Program for Scientific Translations. Published for the National Science Foundation, Washington. 250 pp. Burrough, D. E. and R. P. Harbage 1953 Performance of a corn picker-sheller. Agricultural Engineering 34:21-22. Byg, D. M., W. E. Gill, W. H. Johnson and J. E. Henry 1966 Machine losses in harvesting ear and shelled corn. Paper NO. 66-611 presented at the 1966 winter meeting, American Society of Agricultural Engi- neers, Chicago. Cutler H. C. and M. C. Cutler 194 Studies on the structure of the maize plant. Annals of the Missouri Botanical Garden 35:301-316. 70 71 Dietz, A. G. H. and F. R. Eirich 1960 High Speed Testing, Vol. I. Interscience Publishers, Inc., New York. 112 pp. Eckstrom, G. A. 1965 Coefficient of cubical thermal expansion and some tensile properties of corn kernels and their relationship to stress crack formation. Thesis for the Ph. D. degree, Purdue University, Lafayette. (Unpublished.) Esau, K. 1966 Anatomy of Seed Plants. John Wiley and Sons, Inc. New York. 376 pp. Finan, J. 1950 Maize in the Great Herbals. Chronica Botanica CO., Waltham, Mass. 191 pp. Frey-Wyssling, A. 1957 Macromolecules in Cell Structure. Harvard University Press, Cambridge. 112 pp. Goss, J. R., R. Bainer and R. G. Curley 1955 Field tests of combines in corn. Agricultural Engineering 36:794-796. Grantham, A. E.- 1917 The relation of cob to other ear characters in corn. Journal Of the American Society of Agronomy 9:201-217. Grobman, A., W. Salhuana and R. Sevilla 1961 Races of Maize in Peru. Publication 915, National Academy of Sciences, National Research Council, Washington, D. c. 374 pp. Guidry N P. 1965 A Graphic Summary of World Agriculture. Misc. Publication NO. 705, Economic Research Service, United States Department of Agriculture, Wash- ington.’ 64 pp. Hall, G. E. 1961 Departmental Report, Department of Agricultural Engineering, Ohio Agricultural Experiment Station, Wooster. 72 Hopkins, D. F. and G. E. Pickard 1953 Corn shelling with a combine cylinder. Agri- cultural Engineering 34:461-464. Jain, M. L. 1966 Characteristics and analysis of corn ear failure. Thesis for the degree of M. S., The Ohio State University (Unpublished). Johnson, W. H. and B. J. Lamp 1966 Principles, Equipment and Systems for Corn Harvesting. Agricultural Consulting Associates, Inc., Wooster, Ohio. 370 pp. Kiesselbach, T. A. 1949 The structure and reproduction of corn. Research Bulletin 161, University of Nebraska Agricultural Experiment Station, Lincoln. 96 pp. Kiesselbach, T. A. and E. R. Walker 1952 Structure of certain specialized tissues in the kernel of corn. American Journal of Botany 39: 561-569. Kiesselbach, T. A. 1960 The significance of Xenia effects on the kernel weight of corn. Research Bulletin 191, Nebraska Agricultural Experiment Station, Lincoln. Lamp, B. J., Jr. 1959 A study of the threshing of wheat by centrifugal force. Thesis for the degree of Ph. D. Michigan State University, East Lansing. (Unpublished) Lenz, L. W. 1948 Comparative histology of the female inflorescence of Zea mays L. Annals of the Missouri Botanical Garden 35:353-376. Love, H. H. and J. B. Wentz 1917 Ear characters and yield of corn. Journal of the American Society of Agronomy 9:315-324. Metcalfe, C. R. 1960 Anatomy of the Monocotyledons: I Graminae. Oxford University Press, London. 731 pp. Miles, 3. R. 1956 Maturity of corn in relation to field shelling. Proceedings of Conference on Field Shelling and Drying Corn, U.S.D.A. A77.2:C81. Chicago. A" 73 Miles, S. R. and E. E. Remmenga 1953 Relations of kernel, cob and ear moisture in dent corn. Purdue University Agricultural Experiment Station Bulletin 599, Lafayette. Mohsenin, N. N. 1966 Physical Properties of Plant and Animal Materials. Part One, Volume One. Structure, Physical Charac— teristics and Rheological Properties. The Penn- sylvania State University. 305 pp. Moustafa, S. M. A. 1966 Mechanical properties and structural stability Of the wheat plant. Thesis for the degree of Ph. D., Michigan State University, East Lansing. (Unpublished) Nickerson, N. H. 1954 Morphological analysis of the maize ear. American Journal of Botany 41:87-92. Poindexter, C. C. 1903 The development of the spikelet and grain of corn. The Ohio Naturalist 4:3-9. Sass, J. 1960 The development of ear primordia of Zea in relation to position on the plant. Iowa Academy of Science 67:82-84. Sehgal, S. M. and W. L. Brown 1965 Cob morphology and its relation to combine har- vesting in maize. Iowa State Journal of Science 39:251-268. Sharman, B. C. 1942 Developmental anatomy of the shoot of Zea mays L. Annals Of Botany 6:245—282. Tolstov, G. P. 1965 Fourier Series. Translated from the Russian by R. A. Silverman. Prentice—Hall, Inc., Englewood Cliffs. 336 pp. Toulmin, S. 1961 Foresight and Understanding. Indiana University Press, Bloomington. 115 pp. 74 U. SO D. A. 1965 Losses in agriculture. Agricultural handbook 291. Agricultural Research Service, Washington, D. C. 120 pp. U. S. D. A. 1967 Crop production: 1967 annual survey. Statistical Reporting Service, CrOp Reporting Board, Washington, D. C. 110 pp. Waelti, H. and W. F. Buchele 1967 Factors affecting corn kernel damage in combine cylinders. Paper no. 67-631 presented at the 1967 Winter Meeting, American Society of Agri- cultural Engineers, Detroit. Weatherwax, P., 1917 The development of the spikelets of Zea mays. Bulletin of the Torrey Botanical Club 44:483-496. Weatherwax, P. 1923 The Story of the Maize Plant. The University of Chicago Press, Chicago. 247 pp. Weatherwax, P. 1935 The phylogeny of Zea mays. The American Midland Naturalist 16:1-71. Weatherwax, P. 1954 Indian Corn in Old America. The Macmillan Co., New York.' 253 pp. Wenholz, H. 1916 A form for describing maize ears. Agricultural Gazette of New South Wales 27:701-702. White, R. K. 1966 1966 Swelling stresses in corn kernels as influenced by moisture sorption. Thesis for the degree of M.S. The Pennsylvania State University, University Park. (Unpublished) Winter, F. L. 1926 Relation Of breaking strength and other cob characters to yield of corn. Journal of the American Society of Agronomy 18:592-596. 75 Wolf, M. J., C. L. Buzan, M. M. MacMasters and C. E. Hist 1952 Structure of the.mature corn kernel. Cereal Chemistry 29:321-382. Yoerger, R. R. 1957 Application of the roller—crusher principle of. processing corncobs.- Thesis for the degree of Ph. D. .Iowa State College, Ames. (Unpublished) Zoerb, G. C. 1958 Mechanical and rheological properties of grain.- Thesis for the degree of Ph. D.- Michigan State University, East Lansing.> (Unpublished) APPENDICES 76 APPENDIX I LITERATURE SURVEY 77 APPENDIX I LITERATURE SURVEY A. Survey Procedure The literature search was initiated by reviewing recent issues of periodicals that normally deal with corn or 'its production. Included in the list of periodicals were the various series of bulletins, circulars and reports issued by State Agricultural Experiment Stations and the United States Department of Agriculture. Latest issues were reviewed first and the search was pursued in the usual reverse chronological order to the year 1945. In some in- stances the review was carried to a much earlier date. Notes were made on the articles related to the subject. The articles located in the periodicals were gleaned for pertinent information. In addition, their lists of references were noted and referred to. Books on the subject Of corn production, plant anatomy and physiology, and harvesting equipment were also reviewed. These were located through the references from the first phase of the study. The author-title and subject indexes of the University Main Library card catalog were also con— sulted. 78 79 The search was concluded by consulting bibliography lists, abstracts and indexes. Keywords always included in this part Of the search were: corn, harvest mahcines, maize, shelling, and Zea mays. B. Periodicals Reviewed-~Genera1 Agricultural Engineering . Agriculture I- Agronomy Journal American Journal Of Botany American Midland Naturalist Biorheology Botanical Gazette Cereal Chemistry Cereal Science Today Crops and Soils Magazine Crop Science Iowa State Journal of Science Journal of Agricultural Engineering Research Journal of Agricultural Science Journal of Agriculture and Food Chemistry Journal of Applied Mechanics Journal of Experimental Botany Journal Of Food Science Journal of the Association of Official Analytical Chemists Nature Proceedings of the Royal Society Of London (Series A and B) Stain Technology The Ohio Journal of Science World Crops C. Periodicals Reviewed--U.S.D.A. and Agricultural Experiment Station Literature The United States Department of Agriculture, together with the State Agricultural Experiment Stations publish many series of pamphlets, circulars, bulletins, handbooks, mono- graphs and leaflets. The material published by the U.S.D.A. could be easily located through the special card catalog in which individual articles are indexed by subject and author. 80 The material published by the various State Agricultural Experiment Stations .required perusal of bound non—indexed volumes. This part of the search was restricted to series issued by the Agricultural Experiment Stations of the states listed below: California ' Georgia Illinois Indiana Iowa Michigan Minnesota Missouri Nebraska Ohio Wisconsin 81 D. Abstracts, Indexes and Bibliographies Agricultural and Horticultural Engineering Abstracts (Dis- continued) Applied Mechanics Reviews Biological and Agricultural Index Dissertation Abstracts Field Crops Abstracts Plant Breeding Abstracts Rubbers: RAPRA Abstracts Science Citation Index Technical Translations (Discontinued after Dec. 1967) U.S.D.A. Library Bibliography of Agriculture Cunningham, J.C. (1948). Maize bibliography for the years 1888-1916 inclusive. Contributions from Iowa Corn Research Institute 3:69—189. Iowa Agricultural Experiment Station, Ames. _ Cunningham, J.C. (1951). Maize bibliography for the years 1937-1945 inclusive. Contributions from Iowa Corn Research Institute 3:194-298. Iowa Agricultural Experi- ment Station, Ames. Hall, Carl W. (1961). Agricultural Engineering Index. Agricultural Consulting Associates, Inc., Wooster, Ohio. ..ld1 .» I' “a“... APPENDIX II TENSION EXPERIMENTS 82 APPENDIX II TENSION EXPERIMENTS Experiments were conducted to determine force- elongation characteristics of the pedicels. Corn ears were selected at random from groups harvested within the 1967 crop season. The corn ears were of the single-cross hybrid, variety 402—2x. Date Of planting was May 20. The corn ears were the same ones that were used for the compression tests Of Chapter 6 and Appendix III. The compression tests were performed at the 1/6,-3/6 and 5/6 positions along the length of the ear, with origin at the base end. The tension tests were performed on 0.45 inch long sections cut from the 2/6 and 4/6 positions on the ear. One kernel out of each section was selected for the tension specimen. Kernels in its immediate vicinity were removed (Figure A2.l), to aid in clamping for the tension test. In order to load the pedicel in tension, the kernels were clamped between coarse sandpaper faces with a clamping force of approximately 6.1 pounds. The cob was clamped between the serrated faces of the Instron type 30—1 pneumatic grips. Clamping force of the pneumatic grips was less than 23 pounds. 83 84 I Figure A2-1-——Exper'imental determination of tensile force- elongation ChaPaCteristics of pedicels. Cob sections were clamped below their diameters. (Photo 67—24) 85 The force-elongation characteristics could be des- cribed as linear up to the point of fracture. The initial portions of these curves were non-linear, but-this was attributed to factors such as straightening Of the pedicels, setting of the grips and interference from the cupule. The force-elongation curves were analyzed (Table A2.1) by extending the linear part of the curves to the elongation axis. Pedicel elongation was computed as that distance between the intercept and the elongation at fracture. The term "elongation error" has been introduced to describe the displacement associated with non-linear elonga- tion of the pedicel. Likewise, the term "force error" was used to indicate the tensile load at which response of the pedicel became linear. Average elongation error was 0.0092 inch. 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The corn was planted on May 20, 1967. Kernel thickness was considered to be that exterior dimension that is obtained by measuring the kernel in a direction parallel to the longitudinal axis of the corn ear. It is usually the smallest of the three dimensions commonly measured on corn kernels. Thickness measurements were made by means of a micro- meter caliper. The caliper was equipped with a ratchet attachment. Results were recorded so that kernel thickness could be related to its position, as counted from the base of the ear. 95 C. Data Analysis The form of the model, suggested the use of the convenient computer STAT series LS Routine prepared by the Michigan State University Agricul- tural Experiment Station. The LS Routine is based on the equation: Y = a + bX If a=O, similarity of the above equation to the model becomes readily apparent. Although the LS Routine could be modified to force a to zero, no such attempt was made. This decision was consistent with the general idea of finding a suitable, yet simple, approximation. D. Results of the Analysis The statistical analyses have been summarized in Table A5.l. Coefficients of determination varied from zero to .87 indicating that the model can be a good one for "uniform" ears. Its failings should also be considered. It is instructive to take the derivative of the equation, 96 with respect to 1. Rate of change of kernel thickness with respect to position, dti/di, is not linear as can be seen from dt i_ .. '51—'41 2 An evaluation of this factor and others suggested the need for a more profound analysis of the problem of simple mathe- matical description than the objectives of this study de- manded. 97 TABLE A-5.l--Summary of regression equations describing kernel thickness as a function of its position along the ear. Ear No., 2 Row No.' a b R F N“ 1,1 .137 .172 .68 62.6 32 1,2 .148 .052 .04 1.018 30 1,3 .134 .199 .55 28.9 26 2,1 .156 .186 .38 18.4 32 2,2 .170 .092 .06 . 1.913 33 2,3 .154 .162 .48 28.0 32 3,1 .184 .002 .00 0 25 3,2 .168 .189 .40 14.0 23 3,3 °167 .208 .54 26.1 24 4,1 .154 .261 .49 36.2 39 4,2 .155 .209 .87 254 39 4,3 .152 .284 .48 30.3 35 5,1 .177 .225 .30 1176 24 5,2 .177 .212 .56 28.9 25 5,3 .181 .170 .25 6.87 23 6,1 .155 .112 .19 4.81 22 6,2 .142 .286 .54 21.9 21 6,3 .143 .166 - .28 8.70 24 *N denotes total number in sample. R2 denotes coefficient of determination. APPENDIX VI GLOSSARY 98 Bract Cupule Glume Herbal Lemma Palea Pedicel Peduncle Period Rachilla Rachis Spikelet 99 —a somewhat modified leaf associated with the repro- ductive structures of a plant._ -designates the depression or alveolus on the cob near the base of which the paired spikelets are attached. It has also been called cucullate depression, corneous cupule or alicole. -one of the two empty bracts at the base of the spikelet in grasses. -a book in which plants are named, described, and often pictured. -the lower of the two bracts enclosing the flower in the spikelet of grasses. Also called the flowering glume. -the upper bract that, with the lemma, encloses the flower in grasses. -one of the ultimate single flower bearing divisions of a peduncle. -a stalk that bears a flower or flower cluster. -an interval, especially one established by repeated or regular recurrence. -a small or secondary rachis, the axis of a spikelet of a grass or sedge. -the elongated axis of an inflorescence. -one of the small few-flowered bracteate spikes that make up the compound inflorescence of a grass or sedge. 100 Viscoelastic-having both viscous and elastic properties in appreciable degree.