Computer aided design of moldboard plough surface

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1 Journal of Agricultural Technology 01 Vol. 8(5: Availale online Journal of Agricultural Technology01, Vol. 8(5: ISSN Computer aided design of moldoard plough surface Mahmoud Soltani * and Javad Taghinezhad Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran. Mahmoud Soltani and JavadTaghinezhad. (01 Computer Aided Design of moldoard plough surface. Journal of Agricultural Technology 8(5: Mouldoard plough is an important agricultural implement and is widely used in primary tillage. An accurate design of plough ottom ased on farmland soil properties is an essential prolem. Therefore, computer aided design of mouldoard must e applied. An algorithm of plough design is presented and carried out in MATLB software and 3D shape of plough was plotted. Introduction Geometric modeling and computer aided design (CAD is recently used in many fields of industry. Design and manufacture of such diverse ojects such as aircraft, cars and ship hulls harvest the enefits of the emerging technology and simultaneous intensive research in the mathematical theory, representation and analysis of surfaces would e studied. As aresult, physical ojects have widely een replaced y computer models. This leads to etter and cheaper products as the latter are simpler to analyze and easier to change than the former (Dimas and Briassoulis, Mouldoard plough is one of the most important tillage implements and is widely used in the world for many years. Designing of moldoard ased on characteristics of farmland is an important prolem, also it is important to descrie and characterize the three dimensional shape of the plough, that facilitate more interesting studies such as analyzing the effect of the soil interactions on the plough (Formato et al., 005. For these studies a computer model of plough is needed. Manual designing of a plough is a time-consuming method and has not adequate accuracy, ut these prolems do not happened in computer aided design. Traditionally, plough design and manufacture have een ased on empirical methods and experiments (Shrestha et al., 001.A new CAD method is necessary to descrie and design of plough surface ased on soil properties of farmland. Several methods were developed for designing of plough y * Corresponding author:mahmoud Soltani; mahsoltani@ut.ac.ir 1545

2 computer. Ravonison and Destain (1999 developed a mathematical expression ased on Bezier's form of cuic surfaces to descrie an existing mouldoard and focused on an algorithm to improve the efficiency of approximation of a theoretical surface and the actual one. Their method was well suited to descriing mouldoard designs. Formato et al (005 studied on the plough mouldoard soil interaction phenomena. They used a detecting system that was ale to determine the X, Y, Z spatial components. The detecting system had three ars located along the three Cartesian axes of the reference system. On each ar, there was a sliding pointer, axially adjustale y a micrometric screw, to measure displacements alongthe X, Y and Z axes, respectively (Fig. 1. Fig. 1. Detected points of a plough surface (Formatoet al., 005 Gutiérrez de Ravé (011 pose was exploration of the geometric algorithms ased on the spline concept. This paper aimed to develop a mathematical algorithm of mouldoard plough designing ased on single directrix curve (Bernakci, 197. The algorithm would e ale to design the plough surface ased on desired characteristics. Material and methods In designing of mouldoard, top view, front view and directrix curve must e drawn that are explained following. Furthermore the three dimensional shape of designed plough is made. 1546

3 Journal of Agricultural Technology01, Vol. 8(5: Front view To plot the front view of plough, coordinates of P 0 to P 6 (Fig. must e otained and joined together. A quadratic line was used to join P and P 3. The coordinates of P 0 was assumed zero. P 1 and P are otained as following: X 1 Δs (1 Where Δs is the reast edge of mouldoard falls from the perpendicular. Z1 H ( X (3 Z a (4 Where a and is depth and width of furrow slice. To otain coordinates of P 3 the sine law was used (see Fig. : ν = sin -1 a ( (5-1 π α = sin ( a sin( + ν / a +.5 (6 π λ = - α - ν (7 Z a = a cos(ν (8 Z = sin( λ + ν (9 Z3 = Z a + Z (10 sin( λ C = a sin( α (11 θ tan 1( (a.5 (1 L ( ( a. 5 (13 C1 L cos( (14 X ( a C C1 (15 The Z value of P 4 is otained y following equation: Z4 S sin( (16 Where δ is cutting angle and S is width of share lade. The slope of line P 3 P 4 is tan (ν and the coordinates of P 3 are known, so: 1547

4 m tan( (17 Z Z3 m( X X 3 (18 ( Z4 Z3 X 4 m X 3 (19 m The Z value of P 5 is 0 and the X value of P 5 is otained y Eq. 0: X 5 (0 Δ is depended on the type of plough (Bernakci, 197. To calculate X component of P 6 the Thales theoremis used and the Z value is otained y following equation: Z6 S sin( (1 By joining of otained points, the front view of moldoard is made. Fig.. The front view of mouldoard. Directrix curve The radius of directrix curve is otained y following equation (Bernakci, 197: R ( ( δ cos(

5 Journal of Agricultural Technology01, Vol. 8(5: Fig. 3. The directrix curve of mouldoard. The Z and X values of arc center that makes directrix curve is otained y Eq. 3: ZO R cos( (3 X o R sin( (4 To calculate coordinates of P 9 following equations are used: X 9 R cos( X O (5 Where Δδ depends on the type of moldoard (Bernakci, 197. Z9 ZO R sin( (6 The lines P 7 P 10 and P 8 P 9 are perpendicular to OP 7 and OP 9, respectively. So the slope of P 7 P 10 and P 8 P 9 are tan( and cot(, respectively. P 10 is otained y intersecting of P 7 P 10 and P 8 P 9. Z 9 + cot( Δδ X 9 X 10 = (5 cot( Δδ + tan( δ tan( X (6 Z10 10 To complete the directrix curve, the lines P 7 P 10 and P 8 P 9 must e divided into desired sections and otained points must e jointed together as a certain order. 1549

6 Top view For designing of the plough the Shchuchkin formula (for cylindrical and helical plough is used. The Shchuchkin equation calculates the value of n as a function of contour line height. In this paper the directrix curve has een inserted in middle of P 0 P 5 and perpendicular to it. X 0 X 5 X a (7 y 0 y y 5 a (8 The components of P i are otained as: X i X a -d cos ( 0 (9 Where d i is the distance etween directrix curve and Z axis at contour line i (Fig.3. y d sin( (30 yi a 0 Fig. 4. The top view of plough. By a point and the slop of a line, the equation of the line can e otained, so the equation of P i1 P i3 is otained as: =cot( ( X - X + y yi1 i i1 i i 1550

7 Journal of Agricultural Technology01, Vol. 8(5: Where i is the setting angle at each contour line and X i1 is the X value of each point that is otained in front view (Fig.. This order is repeated from P 0 P 5 to P 1 P. By jointing of otained point, the top view is plotted. Three dimensional model The X and Z values of each peripheral point of plough surface are otained in front view. By having the X value, the Y component of each point can e calculated y means of directrix curve and top view of mouldoard, so the all needed coordinates of each point can e otained and thus the software can plot the 3D model of designed plough surface. Results and discussions The proposed algorithm of plough designing process was programmed in MATLAB software and was carried out. The needed parameters in this method for designing of plough surface are composed of the width of share lade (S, width ( and depth (a of furrow slice, cutting angle (, distance of plough edge from furrow wall ( s, setting angle ( 0, min, max and Δδ. A typical designed plough y MATLAB is presented in Fig. 5 and Fig. 6. Fig. 5. Tuesday Map view of a typical designed plough surface. 1551

8 Fig. 6. Three dimentional shape of a typical designed plough surface The reverse engineering of plough surface in traditional method needs determining the spatial coordinates of a finite numer of points on the actual working surface. Determining of the 3D coordinates of points on the surface of a moldoard plough also needs a high accuracy detecting system. To perform the 3D model, otained points must e imported into modeling software as stated y Formato et al. (005. In traditional method of moldoard modeling, ecause of manual detecting of coordinates, a few points can e otained. Also the accuracy of modeled surface decreased. By proposed method in this research, we can enhance the accuracy of plough modeling. By this method we can perform the 3D model of plough surface only y measuring of a few characteristics of moldoard. In designing of plough surface, the proposed method allows the designer to change plough surface, soil properties, and operating conditions. With this, Massah and Alimardani (008 also designed and modified an automatic mouldoard profilograph ased on the reverse engineering of plough design. The designed expensive apparatus was ale to draw the profilograms of a 3-D oject as a -D drawing in the same contour lines of mouldoard plough ottom. In this study, the presented algorithmcan design and model a mouldoard ased on necessary conditions relialy. Conclusion This paper presented mathematical expressions of plough surface ased on single directrix curve to design plough as a function of desired 155

9 Journal of Agricultural Technology01, Vol. 8(5: characteristics.the plough surface is represented three dimensionally that can e exported to other analytical software to investigate interaction etween the soil and the plough ottom or predict the needed draught force. This method gives a high accuracy of mouldoard designing and eliminates the human error that occurs in manual designing of plough. References Bernakci, h., Haman, J. andkanafojski, Cz. (197. Agricultural machines theory and construction, Volume. i, U.S Department of Commerce, Springfield, U.S.A. Dimas, E. and Briassoulis, D. ( D geometric modeling ased on NURBS: a review. Advances in Engineering Software 30: Formato, A., Faugno, S. and Paolillo, G. (005.Numerical simulation of soil-plough mouldoardinteraction.biosystems Engineering 9 (3: Gutie rrez de Rave, E., Jime nez-hornero, F.J., Mun oz-piorno, J.M. and Gira ldez, J.V. (011. The geometric characterization of mouldoard plough surfaces y using splines. Soil & Tillage Research 11: Ravonison, N.M. and Destain, M.F. (1994. Parametric cuic equations for modeling mouldoard plough surfaces. Soil & Tillage Research 31: Shrestha, D.S., Singh, G. and Geresenet, G. (001. Optimizing design parameters of a mouldoard plough. Journal of agricultural Engineering Research 78 (4: Massah, J. and Alimardani, R. (008. Design modification of an automatic mouldoardprofilograph. CercetăriAgronomiceîn Moldova 41 (4:5-14. (Pulished in Septemer

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