Analysis of Reaction Forces and Posture of a Bunch of Crop Stalks during Reel Operations of a Combine Harvester

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1 1 Analysis of Reaction Forces and Posture of a Bunch of Cro Stalks during Reel Oerations of a Combine Harvester Y. Hirai 1, E. Inoue 1, K. Mori 1, K. Hashiguchi 2 1 Laboratory of Bioroduction and Environmental Sciences, Deartment of Bioroduction Environmental Science, Faculty of Agriculture Graduate School, Kyushu University, , Hakozaki, Higashi-ku Fukuoka city , Jaan Phone / Fax: of corresonding author: hirai@brs.kyushu-u.ac.j 2 Laboratory of Bioroduction Engineering, Deartment of Bioroduction Environmental Sciences, Faculty of Agriculture Graduate School, Kyushu University, , Hakozaki, Higashi-ku Fukuoka city , Jaan Phone / Fax: of corresonding author: khashi@agr.kyushu-u.ac.j ABSTRACT The urose of the resent study is to clarify reel oerations aroriate to cro conditions, such as a cro s hysico-mechanical roerties and the extent of lodging, from the viewoint of the mechanical interactions between the cros and a combine harvester reel. First, because the gathering rocesses by the reel involve mechanical oerations of forced dislacement, the horizontal and vertical reaction forces of a bunch of cro stalks (rice and wheat stalks) undergoing the forced dislacement were measured. Further, a bunch of cro stalks, which has conventionally been comlicated in dealing, was considered as a comosition of a single cro stalk, and the reaction forces of cro stalks were analyzed numerically using a differential equation describing deflection, which was derived based on a mechanical model of a cro stalk. As the results, the horizontal reaction forces increased linearly with the increment of forced dislacement (deflection), while the vertical ones changed its direction and magnitude deending on relationshi between cro osture and frictional force. The simulated results of the trends of the reaction forces agreed aroximately with measured ones. This suggested that the analytical method of determng reaction forces based on the derived equation could be utilize for investigating reel-cro interactions. This aer also resents osture analysis of a bunch of cro stalks during gathering oerations. Keywords: combine harvester reel, gathering oeration, mechanical model of a cro stalk, a bunch of cro stalks, reaction force, deflection characteristics 1. INTRODUCTION In the field of agricultural machinery, machine tests are usually conducted in the field in order to assess erformance including cro conditions, such as a cro s hysico-mechanical roerties and the extent of lodging. However, it would be advantageous to assess a machine s erformance taking the cro conditions into account at the

2 2 design stage, which would reduce develoment costs and shorten the develoment eriod. In order to imrove the rocess of design and develoment, mechanical interactions between the machine and the cros, which are closely related to erformance and are strongly affected by cro conditions, should be investigated by constructing analytical theories according to various oerations of the harvesting machinery based on a mechanical model of the cro. In the resent study, mechanical interactions between a combine harvester reel and the cro were investigated in order to clarify the gathering oerations of the reel aroriate to secific cro conditions. Several investigators have studied a variety of hysico-mechanical roerties of biological materials for the urose of alying them to machine design, mechanical rocesses and lodging roblems. O Dogherty et al. (1995) examined the effects of wheat straw s maturity, stem internode osition, and moisture content on hysical (diameter and wall cross-sectional area) and mechanical (shear strength, tensile strength, Young s modulus, and modulus of rigidity) roerties. Gawda (1978) measured the Young modulus of cereal stalks along the stalk s length during earing and at full maturity using an ultrasonic method. Gowin (1980) alied a measurement method involving holograhic interferometry for determng the elasticity modulus of wheat stalks. Gowin (2000) roosed accurate methods for determng cereal stalk cross-sectional area and the moment of inertia of the stalk cross-section using a microscoic method and image analysis. Moustafa et al. (1968) discussed the stability of the wheat lant in terms of the buckling load and investigated the effect of maturity on the lant s elastic and visco-elastic arameters. Muller (1988) discussed the stability of the wheat-stalk based on the bending and torsional rigidity measured in each of its internodes. Szot and Skubisz (1984) evaluated winter wheat stalk elasticity including the influence of the root system, and investigated the effect of lant maturity on lant elasticity. As stated above, the mechanical characteristics and behaviors of biological material, which can be alied to the machine design, have been investigated, yet instances of their actual alication to design are very few, and machine erformance is still assessed based on field tests. One reason for the low number of real alications is the existence of very few studies focusing on the mechanical interactions between cros and the machine during actual oerations. Namely, further studies regarding the mechanical behavior of biological materials involved in machine oerations are indisensable to the alication of the above investigations to machine design. Gathering erformance of the combine reel is affected by control arameters such as height and seed of the reel, and the location of the cutter bar in relation to the reel, and these arameters must be adjusted according to cro conditions. However, current oerating manuals rovides only a slight descrition of the adjustment oints of these arameters, the erformance deends mainly on the skill of oerators. The clarification of effective reel oerations can contribute to more effective control under secific cro conditions, to the develoment of a control system which rovides stable erformance, and also to reduction of the burden of the oerators. Further, investigation of reel-cro interactions based on the mechanical model can lead to assessment of the erformance from various asects such as head loss, ower requirement and smooth feed of cut stalk into the auger. Previous studies focusing on reel oerations have mainly shown the reel s

3 3 geometric motion and the results of field tests. Esaki (1955) derived the equation describing the trajectory of the reel s motion and roosed a formula for determng the location of the cutter bar in relation to the reel. As well, Esaki reorted the results of field tests under various velocity ratios, reel oerating heights, and locations of the cutter bar. Sakai et al. (1993) derived a formula for determng the location of the cutter bar in relation to the reel under the condition of a standing single cro. Further, in order to determine a arameter necessary for utilizing the formula, Oduori et al. (1993) exerimentally established a mathematical relationshi between the ratio of rice stem deflection to the acting height of a deflecting force and a stem deflection angle. The above studies are valuable for determng the design arameters of a reel, yet they are alicable only to limited conditions due to an only slight theoretical consideration of the mechanical interactions between a combine reel and cros. Thus, the investigation of reel-cro interactions based on a mechanical model of a cro is indisensable. The combine harvester reel feeds cro stalks into the auger while changing the location of its oeration by its rotational motion. In this oeration, reel-cro interactions, which involve the change of both external force of the reel (reaction force of the cro stalks) and cro osture, affect the behavior of the cut stalk; that is, these factors affect the oerational erformance of the reel. Thus, the authors (Inoue et al., 1998) alied a large deflection equation regarding an elastic beam to a rice stalk, and discussed the alication to large deflection by the reel oerations. Further, a mechanical model of a cro stalk with a heterogeneous cross-section based on bending theory regarding an elastic beam was roosed, and also a calculation method of flexural rigidity for materials with heterogeneous cross-section was insected by deflection tests using iano wire (Hirai et al., 2000). An extended model that takes into account the effect of a cro ear was roosed, and the relationshis between the deflection and deflection force (horizontal force comonent) acting on a bunch of cro stalks during the reel oerations were analyzed under a standing cro condition (Hirai et al., 2002). It was suggested that the model was useful for investigating reel-cro interactions, and also that the analytical accuracy of the deflection force would be increased by considering the effect of the vertical force comonent and stalk s tial osture. In the resent study, the horizontal and vertical reaction forces of a bunch of cro stalks (rice and wheat stalks) undergoing forced dislacement were measured through a series of exeriments involving the gathering oerations of a reel. Further, a differential equation describing deflection, which took into account the vertical force comonent, was derived based on the mechanical model of a cro stalk, and was used for numerical analysis of the reaction forces. In the analysis, the effect of friction was also considered. The simulated results of the trends of the reaction forces aroximately coincided with the measurements. This suggested that the analytical method of determng reaction forces based on the derived equation could be utilized for investigating reel-cro interactions. This aer also resents osture analysis of a bunch of cro stalks during gathering oerations.

4 4 Notation D j : flexural rigidity of the j th internode, kn mm 2 E: x coordinate at acting oint of concentrated load, mm E l : length of an ear, mm f: frictional force, N F x : horizontal reaction force, N F y : vertical reaction force, N h : height at the loading oint, mm i: the number of cro stalks L: length of a cro stalk, mm M: bending moment acting on a cro stalk, N mm n: number of nodes or internodes from fixed end N: total number of cro stalks P: load acting on a cro stalk, N P n : normal force acting on a cro stalk, N P r : normal reaction force, N P t : tangential force acting on a cro stalk, N W: weight of an ear, N x i, y i, z i : reference coordinates of cro stalks, mm x j, y j : x, y coordinates at the j th node, mm x, y : x, y coordinates at loading oint, mm x t, y t : x, y coordinates at the ti of a stalk, mm θ : deflection angle at loading oint, rad θ t : deflection angle at the ti of a stalk, rad 2. Exerimental system and method 2.1 Exerimental system Exerimental system involving the reel oerations is illustrated in Figure 1. This system is comosed of an L-shaed sensor, oil-hydraulic aaratus, low ass filter (KYOWA, LF-303A), strain amlifier (KYOWA, DPM-612B), data-recorder (TEAC, DR-C1MK2), notebook comuter (TOSHIBA, SA65C/4), digital video camera (SONY, DCR-VX1000), and tested material. The dimensions of the L-shaed sensor made in this exeriment and the arrangement of strain gauges bonded to the steel body are shown in Figure 2. Four ieces of strain gauges were mounted on the body around each circular hole involving stress concentration. The bridge circuits were comosed of each

5 5 set of them, and voltage signals due to the change of strain was oututted. Thus, the L-shaed sensor is caable of sensing two mutual erendicular force comonents. The L-shaed sensor attached to the rod of oil-hydraulic cylinder is controllable for horizontal motion and its seed by oil-hydraulic um. The loading seed is measured by tracing reflector tae ut on the cylinder rod using image data. The acting height of the sensor is adjustable using a stand. The material cro stalks tested comes in contact with the aluminum roller equied with the ti of the sensor, while they are deflected by the horizontal motion of the sensor. At that time, high frequency signals due to a slight vibration during horizontal movement are removed from original electrical signals of the sensor by a low ass filter, and then the signals are amlified and recorded on a data recorder, which converted analog into digital data automatically. Data acquisition system is shown in Figure 3. The cro osture during the exeriment is recorded by means of a digital video camera. F F x F y L-shaed sensor Oil-hydraulic cylinder Oil-hydraulic um Forced dislacement Reflector tae Y O Aluminum roller Z X O 10 mm 10 mm Z Rice stalks arrangement at base Low ass filter Digital video Camera Strain amlifier X O 14 mm 14 mm Z Wheat stalks arrangement at base Notebook comuter Data recorder Figure 1. Exerimental system involving reel oerations and arrangement of a bunch of cro stalk X

6 Strain gauges Figure 2. Dimensions of the L-shaed sensor and the arrangement of strain gauges (all dimensions are in mm) Strain gauges Bridge circuit Low ass filter Strain amlifier Notebook comuter Figure 3. Data acquisition system Data recorder 2.2 Exerimental method Measurements were made on Mineasahi variety of rice stalks and Chikugoizumi variety of wheat stalks. The secimens were selected randomly from 0.5 are area field of Kyushu University in Fukuoka, Jaan. The roots were removed and a bunch of cro stalks (21 ieces of rice stalks and 16 ieces of wheat stalks) were fixed to a iece of wood at their base and arranged in the same manner as they would be in a field as shown in Figure 1. The base osition closest to the sensor was defined as origin. Samling was carried out in 2001 from 15 to 23 October and in 2001 from 29 May to 7 June for the rice and wheat, resectively. The acting height of the sensor was arranged according to the actual oerational height of the reel, which was 70~80 % of the aearance height of the cro stalks. The cro stalks were deflected by the horizontal motion (forced dislacement) of sensor, while at that moment two mutual erendicular comonents of reaction forces were measured simultaneously. The tests were conducted twice for each material so that the material would not involve changes of the hysical roerties of the cro stalks such as fatigue and destruction, and each six materials of a bunch of rice and wheat was measured. Two sets of data were obtained for each material, and one data set among them was used for assessing the accuracy of this exeriment. This exeriment was conducted under a quasi-static condition; the seed of the sensor was about 10 mm s -1. The reel acts dynamically on the cro stalks at a eriheral seed of about 1.5 m s -1 under standard oerations, though the basic oeration of the reel is the

7 7 oeration, which deflects the cro stalks. Thus, it is indisensable to establish an equation which exresses the relationshi between the load acting on the cro stalk and the deflection (differential equation describing deflection), and to examine the alication range of the equation. In a future study, the range will be discussed through comarison with exerimental results under dynamic conditions, and the motion equation will be derived from a differential equation describing deflection. Following this exeriment, a deflection test for determng the flexural rigidity of each cro stalk comosing the bunch was carried out. 2.3 Deflection test An illustration of the measurement system for deflection test is rovided in Figure 4. This system is comosed of markers, a line-shift camera (COSMO SYSTEM, LCIID-5000B), an image-rocessing aaratus (FAST, CSC901b), a monochromatic monitor, halogen lams, and a ersonal comuter (NEC, PC9801). The line-shift camera rovides an image in two dimensions by driving the CCD elements through a steing motor. The image-rocessing aaratus converts the image into gray tones and can control the range of gray tones in order to distinguish an object. The ersonal comuter collects data regarding the makers center coordinates, which are recognized by image rocessing, through a RC-232C interface. Criterion marker Height x Line-shift camera Deflection y Halogen lam Image-rocessing aaratus Node1 (x 1, y 1 ) Node2 (x 2, y 2 ) (x 0, y 0 ) Cro stalk Marker Monochromatic monitor RS-232C h Load P Personal comuter Figure 4. Measurement system for deflection test Node3 (x 3, y 3 ) In this measurement, the theory of segmentation, in which images are segmented into either white (0) or black (1) values, was alied in order to recognize the markers digitally. Images segmented were analyzed by using a rogram made of C language. The markers center coordinates were calculated based on the geometrical moment of the recognized area of the markers. The deflection of a stalk was calculated by the dislacement from the criterion marker to each marker bonded to the stalk, and the

8 8 height was calculated based on the distance between each marker. The deflection and height of each stalk node was measured while the load was acted on the ti of the stalk. The flexural rigidities of each internode and an average value were calculated using Eqn (1) emloying data obtained from the deflection test. where, (I) n = 1 dy = dx (II) n 2 ( x dy dx = f ( x, D) = f ( x, D n 1 n f ( x, D ) x x ) n ) + 2 n n 1 j= 1 2 x h x 2 { f ( x, D ) f ( x, D )} j j 2 2 D x h 2 x P and: D j is the flexural rigidity of the j th internode; h is the height at the loading oint; n is number of nodes or internodes from fixed end; P is the load acting on a cro stalk; x j, y j are the x, y coordinates at the j th node. Now, the Eqn (1) is a differential equation for the deflection angle. To calculate the deflection using this equation, the Runge-Kutta Method was alied. The data regarding rice and wheat stalk flexural rigidity, length, weight, and moisture content are shown in Table 1. In Table 1, the figures in arentheses reresent the standard deviation. The flexural rigidity and length of the stalks were measured for all stalks comosing the bunch, and the standard deviation was calculated. The weight, length of the ear, and moisture content were exressed as the average values obtained from five samles of the bunch. j j+ 1 (1)

9 9 Table 1 Data regarding rice and wheat stalk flexural rigidity, length, weight and moisture content Rice stalk No.1 Internode1 Internode2 Internode3 Whole Ear Flexural Rigidity, kn mm (12.9) Length, mm 175 (48) 43.3 (21.9) 232 (65) 12.1 (3.4) 30.1 (9.2) Weight, N Moisture Content, % w.b Rice stalk No.2 Internode1 Internode2 Internode3 Whole Ear Flexural Rigidity, kn mm (10.3) Length, mm 208 (46) 25.3 (10.6) 187 (10) 368 (40) 9.2 (1.7) 775 (50) 22.9 (5.2) Weight, N Moisture Content, % w.b Wheat stalk No.1 Internode1 Internode2 Internode3 Whole Ear Flexural Rigidity, kn mm (9.2) Length, mm 198 (46) 48.8 (20.6) 244 (12) 326 (22) 16.4 (5.3) 720 (40) 28.8 (8.1) Weight, N Moisture Content, % w.b Wheat stalk No.2 Internode1 Internode2 Internode3 Whole Ear Flexural Rigidity, kn mm (12.1) Length, mm 174 (47) 56.6 (34.4) 238 (10) 336 (29) 20.2 (6.5) 778 (49) 31.1 (11.6) Weight, N Moisture Content, % w.b NOTE: Figures in arentheses reresent standard deviation, the number of internode indicate order from the base. 347 (35) 3. Analysis of reaction forces 3.1 Mechanical model of a cro stalk and differential equation describing deflection The differential equation describing deflection was derived based on the mechanical model of a cro stalk as shown in Figure 5. In this model, a sectional heterogeneity of a stalk was exressed as the different flexural rigidity D j of each internode (subscrit j is the number of internode), and the effect of an ear was considered to be a 759 (44)

10 10 load concentrated at the ti of the stalk. In the resent study, the flexural rigidity D θ t Y was exressed as one arameter, while it was E generally exressed as the roduct of the P t E l modulus of the stalk s elasticity and its θ moment of inertia. The center of the ear W D 3 (x t, y t ) length was assumed to be the acting oint Forced of the concentrated load. The resultant dislacement P force acting on a cro stalk undergoing (x, y ) n forced dislacement is comosed of normal D 2 force P n and tangential force P t. The tan- L gential force P t gives the elongation on the cro surface at its loading oint, but the effect on the bending was considered to be D 1 very slight. Thus, only the bending moment X due to the normal force and concentrated O load was considered, and a differential Figure 5. Mechanical model of a cro stalk equation describing deflection was derived. undergoing forced dislacement The bending moment acting on the cro stalk is obtained as follows. (I) 0 y y M = P cosθ ( y (II) y n y y t y) + P n sinθ ( x x) + W ( E x) M = W ( E x) Here, E = x t + ( E l sinθ t / 2) Further, the differential equation describing deflection of a cro stalk is derived from relation between curvature and bending moment as follows d x M dx = (3) dy D j dy where: E is the x coordinate at acting oint of concentrated load; E l is the length of an ear; L is the length of a cro stalk; M is the bending moment acting on a cro stalk; P n is the normal force acting on a cro stalk; P t is the tangential force acting on a cro stalk; W is the weight of an ear; x, y are x, y coordinates at loading oint; x t, y t are x, y coordinates at the ti of a stalk; θ is the deflection angle at loading oint; θ t is the deflection angle at the ti of a stalk 3.2 Calculation method of reaction forces using the differential equation The reaction force of a cro stalk undergoing forced dislacement is comosed of normal reaction force P r and frictional force f. The normal reaction force P r, which is balanced with normal force P n, was calculated using Eqns (2) and (3). The frictional force, which was the resistance force against tangential force P t, was assumed to (2)

11 11 be equal to maximum static frictional force, and the frictional force was calculated by means of f = µp r using the coefficient of static friction µ. The frictional force f was considered ositive uward along the tangential direction, and the direction of the reaction force was taken to be ositive following arrow illustrated in Fig.1. Thus, reaction forces Fx, F y in horizontal and vertical directions are obtained as follows. Fx = Pr cosθ f sinθ (4) Fy = Pr sinθ + f cosθ The flow chart for calculation of the reaction forces is shown in Figure 6. First, data regarding hysical roerty of each cro stalk, the reference coordinates of the i th cro stalk (x i, y i, z i ), total number of cro stalk N, loading oint (x, y ) (location of the sensor) are inutted. Next, the current deflection of the i th cur cro stalk is calculated based on the relationshi between the location of the sensor and reference coordinate of the cro stalk. In this calculation, a standing condition of the cro stalk was assumed. Namely, distribution of cro stalks at acting height of the sensor is assumed to be the same as that at base, and deflection of each cro stalk was calculated from difference of x coordinate between at the sensor s height and at the base. Further, the normal force P n is calculated using three tial values of both deflection and deflection angle at the ti of a stalk, and an tial value of de- flection angle at loading oint. Namely, the tial value of is renewed re- cal eatedly until the calculated deflection x aroaches to current deflection x cur to a sufficient extent while cro s shae is assumed to have deflection and deflection angle given tially (three tial values). Therefore, in the next ste, the validity of the cro s shae assumed tially (given three tial values) must be determined. The given three cal cal cal tial values,, must be close to,, calculated under converged to a sufficient extent. Thus, normal forced Pn and deflection angle at loading oint P n θ x t θ t θ θ i x t x t are determined, and each comonent of reaction forces of one cro stalk is calculated at an arbitrary sensor dislacement (location). This series of calculations was conducted for each cro stalk comosing the bunch. The reaction forces of the bunch of cro stalks at each sensor dislacement were calculated from the summation of the reaction forces of all cro stalks. The dislacement of the sensor was defined as the horizontal dislacement from the base of the cro stalk closest to the sensor. The differential equation was solved by means of the Runge-Kutta Method, and the tial values were renewed by means of the Gauss-Newton Method. The calculation of the deflection by the Runge-Kutta method has been verified through deflection tests using a cantilever iano wire shown in figure 4 (Inoue et al. 1998). In this analysis, interactions between the cro stalks were not considered. Considering the contact surface of the aluminum roller used in this exeriment, a coefficient of static friction 0.4 (material: rice stalk, surface: steel sheet) and 0.3 (material: wheat stalk, surface: galvanized steel sheet) were cited for rice and wheat stalks, resectively (Esaki, 1986). In his measurement, the material is held in a container loaded with weight, and its surface is mounted on the steel sheet. The contact surface between the material and the steel sheet is drawn θ t θ t θ x i P n i

12 12 by weight through a ulley. The weight is measured at the moment when the surface slides, and the static frictional coefficient is determined. D ij :flexural rigidity of the j th internode of the i th cro stalk E l : length of the ear l i : length of the i th cro stalk N: total number of cro stalks (x i, y i, z i ): reference coordinates of the i th cro stalk (coordinates at base) (x, y ): coordinates at loading oint (acting location of the sensor) W: weight of the ear Start Inut data Calculate current deflection of the i th cro stalk cur x i Inut/Renew tial values of deflection and deflection angle at the ti of the stalk,, defection angle at loading oint x t θ t θ Inut/Renew t ial value of normal load P n Calculate deflection at loading oint cal x i No x cal i x Yes Calculate deflection and deflection angle at the ti of the stalk,, cal deflection angle at loading oint cur i θ cal cal x t θ t x cal t x, θ θ, θ t cal t t cal θ No Yes Calcu late/outut P n, θ, F x, F y No i=n Yes Sum F x, F y /Outut F x (x ), F y (x ) End Figure 6. The flow chart for calculation of reaction forces

13 13 4. Results and discussion 4.1 Comarison between numerical analysis and measurement results of reaction forces Comarison between numerical analysis and measurements of horizontal and vertical reaction forces are shown in Figures 7 and 8. The deflection of the horizontal axis in the figures reresents the horizontal dislacement of the sensor from the base of the cro stalk closest to the sensor (the origin was defined as shown figure 1). The materials tested were not comletely standing cros (having some tial osture), and at the origin some force comonents were measured since the tial osture inclined toward the negative direction on the X axis. Because relationshis between deflection and reaction forces from the origin were examined in the resent study, the effect before the origin (the effect at negative x) was not considered; the force comonents measured before the origin were removed, and reaction forces at the origin were regarded as 0. The direction of each reaction force was taken to be ositive following arrow illustrated in Figure 1. The cro s Number in Figure (e.g., rice stalk No.1) corresonds to cro s number in Table1. At first, measurement results are examined. The horizontal reaction forces linearly increased along with the increment of the sensor s dislacement, while the vertical reaction forces showed one negative eak, and then increased linearly. The measurement results of the vertical reaction forces are exlained as follows. At the range of aroximately 0 to 100 mm, the vertical forces take negative values because the vertical comonent of the frictional force directed downward along the tangential direction is larger than the vertical comonent of the normal reaction force. Also, the sensor s dislacement, at which the vertical reaction forces shift from negative to ositive values, was the location where the vertical comonent of the normal reaction force was beyond that of the frictional force because of the stalk s osture (large curvature). The linear increment of the horizontal forces in the range from 0 to 40 mm in which the cro stalks were arranged, was considered to be caused mainly by the interactions between the cros and the difference of distribution between the loading oint and the base due to the cro s tial osture. Namely, the cros are ushed together due to the interactions between the cro stalks, and the sensor already acts on some cro stalks at the origin due to the tial osture of the cros. Consequently, the horizontal reaction forces changed linearly regardless of the arrangement of the cro stalks at the base. Next, comarison results with numerical analysis are shown. Referring to results of rice stalk shown in Figure 7, simulated results of horizontal comonent were low values in comarison with the measurements esecially in the range of the sensor s dislacement from 0 to 40 mm in which a bunch of cro stalks was arranged at the base. The main reason is that analysis of reaction force was conducted under a standing condition of cro stalks though the cros stalks have actually some tial osture. Namely, the distribution of the cro stalks at loading oint was assumed to be same manner as that of base and the reaction force was calculated based on difference between coordinate at base and the sensor s dislacement, thus the simulated values had a certain amount of error. The results of vertical comonent comaratively had a tendency to coincide with measurements. Simulated results for wheat stalks shown in figure 8 reduced

14 14 the error with measurements comared with the case of rice stalk. In case of No.1 wheat stalk as shown in left side of figure 8, the horizontal value had a certain amount of error throughout, but the increment coincided considerably with measurement. Some error due to tial osture at the beginning of simulation only kees until end of simulation, and the analytical accuracy would be increased by considering the effect of tial osture. In case of No.2 wheat stalk, simulated result had good consistence with measurement because tial osture was close to a standing condition. As demonstrated by the above results, analytical method used in the resent study requires further develoment in terms of the effect of tial osture, but could aroximately redict valid reaction forces of the bunch of cro stalk. This suggested that the analytical method of determng reaction forces based on the derived equation was useful for investigating reel-cro interactions. Reaction force (N) Measurement Simu lation vertical Deflection (mm) horizontal Reaction force (N) Measurement Simu lation vertical Deflection (mm) horizontal Figure 7. Comarison results between measurement and simulation of rice stalk: left figure: rice stalk No.1 (sensor acting height: 592 mm), right figure: rice stalk No.2 (sensor acting height: 550 mm) Reaction force (N) Measurement Simu lation horizontal vertical Deflection (mm) Reaction force (N) Measurement Simu lation vertical Deflection (mm) horizontal Figure 8. Comarison results between measurement and simulation of wheat stalk: left figure: wheat stalk No.1 (sensor acting height: 630 mm), right figure: wheat stalk No.2 (sensor acting height: 630 mm) 4.2 Posture analysis of a bunch of cro stalks From comarison results of revious section, it was suggested that differential equation describing deflection was useful for investigating reel-cro interactions. In this session, osture analysis of a bunch of cro stalk was conducted using redicted normal

15 15 force by Eqns (2) and (3). The urose of the osture analysis was to obtain data regarding the cro stalk s center of gravity that changes due to the combine s reel oerations during harvesting. The center of gravity of the cro stalk is data indisensable to the clarification of the behavior of the cut stalk and to the investigation of the timing for cutting the stalk. The results of the analysis are shown in Figures 9 and 10. Figure 9 shows results of osture analysis for No.1 rice stalk under an acting sensor height of 592 mm and deflections (dislacement of sensor) of 30, 60, and 90 mm. Figure 10 shows results of osture analysis for No.1 wheat stalk under an acting sensor height of 630 mm and deflections (dislacement of sensor) of 30, 60, and 90 mm. The difference in cro osture in terms of each hysical roerty of the cro stalks and oerating conditions was visualized in three-dimensions. In a future study, the simulated cro osture will be evaluated by comaring actual images. Also, the change of a cro stalk s center of gravity and relationshi between the center of gravity and the location of the cutter bar will be investigated based on the results of the osture analysis. Figure 9. Posture analysis of a bunch of rice stalk (No.1)

16 16 Y X O Z Deflection: 30 mm 60 mm 90 mm Figure 10. Posture analysis of a bunch of wheat stalk (No.1) 5. Conclusions In the resent study, mechanical interactions between a combine harvester reel and cro stalks (rice and wheat stalks) were investigated based on a mechanical model of a cro stalk. The following conclusions were drawn from this study. (1) The reaction forces of a bunch of cro stalks undergoing forced dislacement were measured through a series of exeriments involving reel oerations. As the results, the horizontal reaction force increased with increment of the sensor s dislacement, while the vertical reaction forces changed both its direction and magnitude due to relationshi between frictional force and cro osture. (2) The reaction forces of cro stalks undergoing forced dislacement were analyzed numerically utilizing the differential equation describing deflection based on the mechanical model of a cro stalk. Simulated results had a certain amount of error deending on tial osture of a cro stalk, but their trends aroximately coincided with the measurement. Esecially, the case of wheat stalk had good agreement with the measurement because its tial osture was close to a standing condition. This suggested that the analytical method of determng reaction forces based on the derived equation could be utilize for investigating reel-cro interactions. Further, the analytical accuracy of the reaction forces would be increased by considering the effect of tial osture of the cro stalk. (3) The difference in cro osture in terms of each hysical roerty of the cro stalks and oerating conditions was visualized by means of the cro model. In a future study, the simulated cro osture will be evaluated by comaring actual images, and also the change of the cro stalk s center of gravity due to the reel oerations, and relationshi between the center of gravity and the location of cutter bar will be investigated based on the results of the osture analysis.

17 17 Acknowledgement The authors would like to thank Mr. Tashiro of our technical staff for his helful suort of our exeriment. This research was suorted by a grant from the Scientific Research Fund of the Mstry of Education, Culture, Sorts, Science, and Technology of Jaan. References Esaki H Studies on harvesting machines (X): Some data for the design of reel. Journal of the Jaanese Society of Agricultural Machinery, 17(1): (In Jaanese) Esaki H Grain harvester Jaan: Isebu. (In Jaanese) Gawda H Attemt at Alying the Ultrasonic Method for Determng the Young Modulus of Cereal Stalk. ZESZYTY PROBLEMOWE POSTEPOW NAUK ROLNICZYCH, z. 203: Warszawa. Gowin J Determination of Wheat Stalk Modulus of Elasticity by means of Holograhic Interferometry. In Proc. II. Int. Conf. On Physical Proerties of Agricultural Materials, 1-8. Godolo, Hungary August. Gowin J Geometry of Cereal Stalk Cross-Section. International Agrohysics, 14: Hirai Y., E. Inoue, K. Hashiguchi, Y. K. Kim, S. Inaba and K. Tashiro Examination of Calculation Method for Flexural Rigidity of Cro Stalks. In Proc. 3rd Int. Conf. on Agricultural Machinery Engineering (Korean Society for Agricultural Machinery), Vol. II: Seoul, Korea November. Hirai Y., E. Inoue, K. Mori and K. Hashiguchi Investigation of Mechanical Interaction between a Combine Harvester Reel and Cro Stalks. Biosystems Engineering, 83(3): Inoue E., Y. K. Kim, K. Hashiguchi, T. Okayasu and J. Kashima Mechanical Characteristics of Rice Stalk. Journal of the Jaanese Society of Agricultural Machinery, 60(2): (In Jaanese) Moustafa S. M. A., B. A. Stout and W. A. Bradley Elastic and Inelastic Stability of a Biological Structure. Journal of Agricultural Engineering Research, 13(1): Muller Z An Investigation on Mechanical and Geometrical Proerties Influencing the Stability of Wheat-Stalk. Physical Proerties of Agricultural Material and Products, Edited by R. Reznicek, Washington: Hemishere Publishing Cororation. Oduori M. F., J. Sakai and E. Inoue Combine Harvester Reel Stagger-II: Emirical Study on Cro Stem Deflection and Alication of the Results for Reel Stagger De-

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