Vol. 49, No. /6 STUDY ON THE SCOOP ANGLE CHARCTERISTICS OF A HANDHELD TILLER S ROTARY BLADE / 微耕机用旋耕弯刀正切刃背角特性研究 Ms. Stud. Eng. Zang Y.H. ), As. P.D. Eng. Yang L. ), Ms. Stud. Eng. Niu P. Ms. Stud. Eng. Li S.T. ), Prof. P.D. Eng. Xie S.Y. ), Prof. Eng. Cen X.B.* ), Prof. P.D. Eng. Yang M.J.* ) ) Soutwest University, College of Engineering and Tecnology / P. R. Cina; ) Key Laboratory of Modern Agricultural Equipment, Ministry of Agriculture / P. R. Cina Tel: 86388359; E-mail: cxibi@6.com; ymingjin@swu.edu.cn Keywords: andeld tiller, rotary blade, scoop angle, plane conversion ABSTRACT A matematical model of scoop angle of te sidelong edge of a andeld tiller s rotary blade was establised by plane conversion and angle cange. Te effects of cornerite of te sidelong edge and bending angle of te blade on scoop angle were studied as well. Te results sowed tat: wit increase of te cornerite, scoop angle linearly increases at large; for sidelong edge of cornerite from 3.5 to 45.4, te corresponding scoop angle increases from 66.6 to 76.6 ; for a position, of same cornerite (oter parameters remain constant), on te sidelong edge, scoop angle increases wit increase of bending angle. 摘要通过平面转换和角度改变, 建立微耕机用刀盘式湿地弯刀正切刃背角的数学模型, 研究了正切刃包角和弯折角对正切刃背角的影响 结果表明 : 随着正切刃包角的增大, 正切刃背角逐渐增大, 呈近似线性关系 ; 当正切刃包角取值范围为 3.5-45.4 时, 对应的正切刃背角为 66.6-76.6 ; 在其他参数不变的情况下, 对于正切刃同一包角位置, 正切刃背角随着弯折角的增大而增大 INTRODUCTION Handeld tillers are mainly used for suc cultivating works as paddy field tillage, upland field tillage, pastoral management and protected agriculture tillage, etc. Te rotating tilling parts, namely te rotavators, are directly driven by te drive saft of a tiller (Peng, et al, 4). Te interaction of rotavator and soil wile soil-tilling functions as bot ands and feet : te ands function includes soil cutting, pulverization, soil turning, soil trowing and soil levelling, etc., and te feet function puses te tiller forward by te soil reacting force from te soil-tilling. Te rotavator consists of some rotary blades and a saft, wit rotary blades mounted on te saft according to a certain arrangement. Te sidelong section and lengtwise section of te rotary blade undertake te soil-tilling task, and te geometric parameters of te blade directly affect te performance of a rotavator and te corresponding andeld tiller (Niu, et al, 5; Yang, et al, 5). Te sidelong section of te blade takes te main responsibility for te soil-tilling and as an important influence on te spraying performance, soil turning and soil trowing. Te scoop angle and clearance angle of te sidelong section of a blade are complementary. Te scoop angle is one of te main parameters of te sidelong section and as an important influence on te soil-cutting resistance and soil trowing (Peng, 4). At te present, many scolars made some extensive investigations on scoop angle or clearance angle of te rotary blade. Sakai et al experimentally studied te effects of scoop angle on soil cutting process, and obtained te reasonable range of scoop angle of te rotary blade under different soil conditions (Sakai, et al, 984; Sakurai, et al, 989). Ding et al studied te effects of blade edge sarpening way and soil cutting mode on te clearance angle of te rotary blade, and obtained te minimum value of clearance angle of wide-type rotary blade wit inside-edged and double-edged curves (Ding, et al, 997). Matin et al studied te variation of blade clearance angle for a conventional blade wit te rotary speed of rotavator from 5 rpm to 5 rpm, analysed te furrowing performance of a straigt blade wit clearance angle 5 at te position of edge curve tip, and pointed out tat te inside-edged blade could enance furrow backfill to improve seed bed, tereby to improve te germination percentage and seeding vigour after sowing (Matin, et al, 5; Matin et al, 6). In tis study, taking te andeld tiller s rotary blade as a case study, te matematical model of te scoop angle of te sidelong edge of te rotary blade was establised by means of plane conversion and angle cange. Te canging rule of scoop angle wit canging of positions of te sidelong edge and te 5
effects of bending angle on te scoop angle caracteristics were studied as well. As a result, te study can provide references to te design calculation, force and vibration reduction, and performance optimization for a andeld tiller s rotary blade. MATERIAL AND METHOD Te rotary blade, adaptable for wetland sticky paddy field tillage, consists of olding section, neck, sidelong section and lengtwise section. It was designed according to Cinese National Standard GB/T 5669-8 Rotary tiller-rotary blades and blade olders, Congqing Standard DB5/T 77-8 Blades of micro-cultivator, and Japanese National Standard JIS B 9-988 (8 confirmed) Blades for tillers. Te main design contents of a rotary blade include edge curve, back edge curve, rotation radius R, maximum cornerite of te lengtwise edge curve θ max, cutting angle, bending angle, bending radius r and tilling widt B, etc., as sown in fig.. Holding section Center of rotation Bending angle θmax Bending radius Rotation radius Back edge curve Bending line Tilling widt Sidelong section Neck section α Lengtwise Sidelong edge Lengtwise section curve edge curve Fig. - Te structure of a rotary blade Considering tat te rotation radius of te andeld tiller s rotary blade is small, a circular sape back edge curve was adopted. A spiral of Arcimedes was adopted for te edge curve, and its equation is as follows: R a R a R, [mm] () n were: R n is rotation radius at a selected point on te edge curve, [mm]; R rotation radius of a rotary blade, [mm]; θ cornerite of te edge curve, [degree]; a and a constants. Te sidelong section takes te main responsibility for te soil-cutting, and geometric parameters directly affect te performance of a rotavator and te corresponding andeld tiller. Wil e rotary tilling, te trajectory of any point on te sidelong edge is a trocoid. Te cross section at any selected point on te sidelong edge was obtained troug a section plane, at te selected point, tat is perpendicular to te rotation axis of te rotary blade, as sown in fig.. β is scoop angle, γ is rake angle, i is sarpening angle, δ is clearance angle or relief angle. Center of rotation nd scoop-surface st scoop-surface γ β i δ st back surface Trocoid Tangent of trocoid Fig. - Te cross-section of sidelong section 6
l Numerical metod was adopted to analyze te caracteristics of te sidelong edge scoop angle of a andeld tiller s rotary blade. A matematical model of te scoop angle was establised by means of plane conversion and angle cange. In order to provide convenience for te build-up of matematical model of te scoop angle, tree planes were defined as follows: plane P is te plane tat contains a selected point on te sidelong edge and is perpendicular to te sidelong edge or its tangent, plane P is te plane tat contains te selected point and is perpendicular to te plane of sidelong section and parallels to te bending line of te rotary blade, and plane P is te plane tat contains te selected point and is perpendicular to te rotation axis of te rotary blade, as sown in fig. 3 and fig. 4. Scoop angle β, sarpening angle i and clearance angle δ are measured in plane P. By plane conversion, dimensions of blade tickness in tese tree planes are e, e and e, respectively, and te dimensions of edge widt, blade edge surface widt, and blade edge surface eigt in tese tree planes are as follows correspondingly: c, c and c ; l, l and l ; and, and. And tere are relations of e =e, c =c and =. e P P ε l c Q Fig.3 - Apparent section P and actual section P of lengtwise section P e e P β γ i' c P P l c Q l P P Fig.4 - Sections P and P Te scoop angle in plane P can be expressed as follows (see fig. 5): were: is scoop angle, [degree]; i ' alf-sarpening angle, and i' i, [degree]; i ', [degree] () te angle between rotation radius and bending line on te sidelong edge, [degree]. 7
E' E Q ' S' i' E y β d α β φ I Q Q S Axis for blade bending O x Fig.5 - Scematic paragrap of scoop angle Half-sarpening angle could be calculated in te cross-section of te cutting edge in P, wit expression as follows: i ' arctan e c, [degree] (3) Because e =e, te tickness of blade e can be expressed as (see Figure 4): e cos e, [mm] (4) were: γ te angle between plane P and P, and γ= - /, [degree]. is bending angle, and it is generally set as º. Similarly, edge widt c can be expressed as: were: c cos c, [mm] (5) Since =, te eigt of te blade edge surface can be expressed as (see fig. 3): cos ε te angle between te plane P and P, [degree]; widt of te blade edge surface, mm, and l e c, [mm]., [mm] (6) 4 By substituting equations (4), (5) and (6) into equation (3), te following expression is establised: i ' arctan ( e c )cos π ( e c) cos( - ) l 4, [degree] (7) For calculating te angle between rotation radius and bending line at te selected point on sidelong edge, a Cartesian coordinate system of te edge curve was establised, as sown in fig. 5. Te selected point Q on te sidelong edge becomes Q by te bending deformation, and teir coordinates are (x, y ) 8
and (x, y), respectively, and (x, y) can be calculated according to te fact: te lengt of te edge curve keeps constant before and after te bending deformation. Ten, te angle between rotation radius and bending line at any selected point on te sidelong section can be expressed as: y arctan( ) x, [degree] (8) were: α te angle between bending line and x-axis, [degree]. By substituting equations (7) and (8) into equation (), te matematical model of scoop angle of te sidelong edge can be obtained as: ( e c )cos y arctan arctan( ) ( e c) x cos( - ) l 4, [degree] (9) RESULTS Taking te andeld tiller s rotary blade as a case study, te caracteristics of te scoop angle of te rotary blade s sidelong edge was studied in tis work. Te parameters of te rotary blade are defined as sown in table, and te edge curve equation of te sidelong section is Rn.58R.8R. Parameters of te rotary blade Table Parameter Value Parameter Value Rotation radius of te blade, R [mm] 8 Blade tickness in plane P, e [mm] 6 Maximum cornerite of lengtwise edge curve, θ max [degree]. Edge widt in plane P, c [mm].5 Cutting angle at θ max, α [degree] 45. Edge surface widt in plane P, l [mm] 8 Bending radius, r [mm] 3 Cornerite at point S, θ S [degree] 3.5 Bending angle, β [degree] Cornerite at point E,θ E [degree] 45.4 Start Radius of spiral of Arcimedes, R [mm] 4.4 Angle between bending line and x-axis, α [degree] 3 According to te matematical model of te scoop angle, scoop angle at positions, wit different cornerites, on te sidelong edge of te defined rotary blade could be calculated. Curves of scoop angle, rake angle and sarpening angle of te sidelong edge wit cornerite were sown in fig. 6. Te sarpening angle is calculated by equation (7), and te rake angle γ is te difference between scoop angle and sarpening angle. Similarly, scoop angle at positions, wit different cornerites, on te sidelong edge of te rotary blade wit different bending angles can be obtained by canging bending angle from 5 to 5º and keeping oter parameters uncanged as sown in table. Te curves of scoop angle wit bending angle were sown in fig. 7. Fig.6 - Curves of scoop angle, rake angle and sarpening angle wit cornerite 9
Fig.7 - Curves of scoop angle wit bending angle As can be seen from fig. 6, wit te increase of cornerite of te sidelong edge, te scoop angle increases. For te rotary blade wit parameters listed in Table, te cornerite of te sidelong edge of te linear section ranges from 3.5 to 45.4, and te corresponding scoop angles linearly increase from 66.6 to 76.6 at large. Note: tis linear section refers to section of sidelong edge starting from point S to E, namely, not including te bending part of te sidelong section. According to literature (Sakai, et al, 984), wit te increase of scoop angle, soil-cutting resistance decreases and te soil-trowing performance degrades, and it is recommended tat te general scoop angle ranges as follows: 4-55 for soft soil suc as sandy or muddy soil, 55-75 for normal soil suc as sandy loam, loam or clay loam, 75-85 for ard soil suc as eavy clay or dry soil. Te scoop angle of te rotary blade wit parameters listed in table ranges witin 66.6-76.6, wic indicates tat te rotary blade is suitable for tilling in loam and clay loam, and is consistent wit te application situation of suc soil type as wet and sticky soil of te rotary blade studied. In fact, te main reason for soil-cutting resistance decrease wit te increase of scoop angle is as follows: te rake angle increases wit te increase of sidelong edge s cornerite, and te larger rake angle, te saper te edge, and as a result, te smaller te soil-cutting resistance. At te same time, te increase of rake angle leads to te decrease of deformation level of te soil out-flowing from te scoop surface, wic results in te decrease of soil-cutting energy consumption. Te deformation decrease leads to te degrading of performance of soil-trowing. However, te clearance angle decreases wit te increase of scoop angle on te sidelong edge, wic results in te increase of friction between back surface of te sidelong section and soil. In addition, wit te increase of cornerite of sidelong edge, te actual sarpening angle decreases, wic makes te blade edge sarper and benefits te blade on te soil-cutting resistance reduction. However, te decrease of actual sarpening angle results in te easy worn-out of te sidelong edge, and te worn-out of edge close to te blade tip is more serious. According to literature (Ding, et al, 4), 5-8% of energy consumption of tilling is consumed by soil-cutting of sidelong section of a rotary blade. As te main angle parameter of sidelong section, te scoop angle as crucial relations wit rake angle and clearance angle of te sidelong edge wile sarpening angle keeps constant. As a result, te scoop angle is an angle parameter tat reflects te compreensive effect of rake angle and clearance angle of te sidelong edge, and it as an important influence on te soil-cutting resistance and soil-trowing performance of te rotary blade. As sown in fig. 7, for a position, wit te same cornerite (wile oter parameters remains constant), on te sidelong edge, te scoop angle increases wit te increase of te bending angle of te rotary blade. Tis is beneficial to te soil-cutting resistance reduction but it results in te soil-trowing performance degrading. Te bending angle falls into range of 5-5º in tis study. At te same time, for rotary blades of different bending angle, te scoop angle increases wit te increase of cornerite of te sidelong edge, wic is consistent wit te aforementioned effect of cornerite on caracteristics of scoop angle. In practical selection, te bending angle sould be determined under compreensive consideration, and te recommended value for te bending angle of a rotary blade is º by Cinese standard GB/T 5669-8.
CONCLUSIONS Te sidelong section of a rotary blade takes te main responsibility for soil-cutting. Te scoop angle is one of te main parameters of te sidelong section and as an important influence on te soil - cutting resistance and soil trowing. Taking te andeld tiller s rotary blade as a case study, te matematical model of te scoop angle of te sidelong edge of te blade was establised by means of plane conversion and angle cange. Te main conclusions are as follows: () Wit increase of cornerite of te sidelong edge, scoop angle linearly increases at large. For sidelong edge of cornerite ranging from 3.5 to 45.4, te corresponding scoop angle increases from 66.6 to 76.6, wic indicates tat te rotary blade is suitable for tilling in loam and clay loam, and it is consistent wit te application situation of te soil type of te rotary blade studied. () For a position, wit te same cornerite (oter parameters remains constant), on te sidelong edge, scoop angle increases wit increase of bending angle of te rotary blade. Tis is beneficial to te soil-cutting resistance reduction. (3) Te scoop angle is an angle parameter tat reflects te compreensive effect of rake angle and clearance angle of te sidelong edge. Te scoop angle as crucial relations wit rake angle and clearance angle of te sidelong edge wile sarpening angle keeps constant, and it as an important influence on te soil-cutting resistance and soil-trowing performance of te rotary blade. ACKNOWLEDGEMENT Te work as been funded by Fundamental Researc Funds for te Central Universities of Cina (XDJK4C33), P.D. Researc Project of Soutwest University (SWU5), and Fund from Key Laboratory of Modern Agricultural Equipment, Ministry of Agriculture, P. R. Cina (6-). REFERENCES [] Ding W., Peng S., (997), Researc on design of wide rotary blade ( 宽型旋耕弯刀的设计研究 ), Transactions of te Cinese Society for Agricultural Macinery, vol. 8, issue 3, pp. 44-48; [] Ding W., Wang Y., Peng S., (4), Analysis on sidelong portion of an up-cut rotary blade ( 反转旋耕 刀正切面分析及参数选择 ), Transactions of te Cinese Society for Agricultural Macinery, vol. 35, issue 4, pp. 4-43; [3] Matin M.A., Desbiolles J.M.A., Fielke J.M., (6), Strip-tillage using rotating straigt blades: effect of cutting edge geometry on furrow parameters, Soil & Tillage Researc, vol. 55, issue S, pp. 7-79; [4] Matin M.A., Fielke J.M., Desbiolles J.M.A., (5), Torque and energy caracteristics for strip-tillage cultivation wen cutting furrows using tree designs of rotary blade, Biosystems Engineering, vol.9, pp.39-34; [5] Niu P., Yang L., Zang Y., Gao B., Li Y., Yang M., (5), Finite element analysis of te rotary blade of a mini-tiller based on ANSYS Workbenc ( 基于 ANSYS Workbenc 的微耕机用旋耕弯刀有限元分 析 ), Journal of Soutwest University (Natural Science Edition), vol. 37, Issue, pp. 6-47; [6] Peng B., (4), Modelling and simulation of soil-cutting dynamics of rotary roller of mini-tiller ( 微耕机 刀辊切土动力学建模及仿真 ), M.S. tesis, Soutwest University, Congqing / P. R. Cina; [7] Peng B., Yang L., Yang M., Guo M., Ye J., Cen J., (4), On connotation analysis and development countermeasures of te mini-tiller standard system ( 微耕机标准体系的内涵分析及其发展 对策 ), Journal of Soutwest Normal University (Natural Science Edition), vol. 39, issue 4, pp.4-46; [8] Sakai J., Lam Van H., Iwasaki K., Sibata Y., (984), Tillage resistance caracteristics of Japanese rotary blades distribution of tilling resistance to te tipless (straigt) blade and bending tip portion of a rotary blade ( ロータリ耕なたづめの耕うん抵抗特性 - 直刃部とわん曲部へのトルク分配 ), Journal of te Japanese Society of Agricultural Macinery, vol. 46, issue, pp. 593-598; [9] Sakurai H., Sakai J., (989), Study on te matematical model of Japanese rotary blades for Computer Aided Design (CAD) - (part ) blades-tip and edged curve portion ( 耕うん用なた刃 CAD 用 数理モデノレ研究 ( 第 報 ) - わん曲部および刃部 ), Journal of te Japanese Society of Agricultural Macinery. vol. 5, issue, pp. 9-35; [] Yang M., Niu P., Peng B., Yang L., Li Y., Cen X., Peng Z., (5), Soil-cutting performance analysis of a andeld tiller s rotavator by Finite Element Metod (FEM). INMATEH-Agricultural Engineering Journal, Vol. 47, issue 3, pp. 3-;
[] ***Ministry of Industry and Information Tecnology of te P. R. Cina, (3), Handeld tillers JB/ T 66-3 ( 微型耕耘机 JB/ T 66-3), Cina Macine Press, P. R. Cina; [] ***Cinese Standard Committee, (8), Rotary tiller - rotary blades and blade olders, GB/T 5669-8 ( 旋耕机械刀和刀座, GB/T 5669-8), Cinese Standard Press, P. R. Cina; [3] ***Congqing Bureau of Quality and Tecnology Supervision, (8), Blades of micro-cultivator, DB5/T 77-8 ( 微耕机配套用旋耕刀, DB5/T 77-8), Congqing, P. R. Cina; [4] ***Japanese Industrial Standards Committee, (8), Blades for tillers, JIS B 9-988 (8 confirmed)( 耕うんづめ, JIS B 9-988(8 確認 )), Japanese Standards Association, Japan.