**2.2 Geometric modeling of transformable moldboard's surface**

Linear surfaces are main use type of in moldboards' working surface. Lines *l* are formatives of cylindrical working surface *Φ*, and all of them are parallel to each other. In considering task they have horizontally position. Working surface *Φ* is formed by directory curve *m*. Type of this curve is planar and it can be given by plane *P*. For frontal moldboard, the plane *P* is located perpendicular to formative lines in the middle of them. This plane intersects the working surface *Φ*, and divides it into two equal *Φ<sup>a</sup>* and *Φ<sup>b</sup>* parts, simultaneously being the symmetry plane of these working surfaces. Let us choose the straight line *k* on the symmetry plane, through which we can carry out the beam of planes. These planes intersect with the *Φ<sup>a</sup>* and *Φ<sup>b</sup>* working surfaces to form intersection curves. Let us define these planes on both sides of the symmetry plane *P*, respectively, *P1,P2, … ,Pn* and *P1* 0 *,P2* 0 *, … ,Pn* 0 , as well as the intersection lines on the working surfaces *Φ<sup>a</sup>* and *Φb*, respectively, curves *m1, m2, … ,mn* and *m1* 0 *,m2* 0 *, … ,mn* 0 . In this case, the angles between planes and plane of symmetry *P*, respectively, denote *α1,α2,...αn*. Each pair of curves *m1,m<sup>1</sup>* 0 *; m2, m2* 0 *; … mn,mn* 0 , formed, respectively, by pairs of planes *P1,P<sup>1</sup>* 0 *;P2,P<sup>2</sup>* 0 *; … Pn,P<sup>n</sup>* 0 , are symmetrical, where *k* is the axis of mirror reflection of pairs of curves on working surfaces *Φ<sup>a</sup>* and *Φ<sup>b</sup>* (**Figure 4a**). Therefore, when the pairs of *Pi* and *Pi* <sup>0</sup> planes rotate together with *Φ<sup>a</sup>* and *Φ<sup>b</sup>* surfaces around the *k*-axis by the corresponding angle *αi*, *Pi*, and *Pi* <sup>0</sup> planes, as well as their *m<sup>i</sup>* and *m<sup>i</sup>* <sup>0</sup> curves are match and form a

**Figure 4.**

*Developing the conception of moldboard with bilateral action working surface. a) geometric model for designing moldboard with bilateral working surface; b) moldboard for outside action; c) moldboard for inside action.*

*2.3.2 Parameters of designed working surface's directory curve*

*Variants of relative positions of directory curve and it's constructive parameters.*

*points of working surface, f – distance between axis and extremely points.*

*DOI: http://dx.doi.org/10.5772/intechopen.89974*

chest or *upper/lower*–on the toe).

**Figure 5.**

**Figure 6.**

**217**

It is necessary to mark the parameters by shape and position of the directory curve *m* of the surface *Φ*. According to the problem, the shape of directory curve *m* is flat and smooth, with a certain curvature and a concave side forward. Since these properties of directory curve remain low during the transformation of the surface, they will be identified as the topological parameters of the curve that determine its shape. Therefore, such surface parameters as its shape and curvature also remain low even when a new surface *Φ<sup>i</sup>* is formed. The position of the curve is defined by two parameters: its offset–*b* and height–*h* of the curve. They are defined as constructive parameters, as they define the design of moldboard. The following variants of mutual arrangement of constructive parameters *m*, determined by the position of characteristic points, can be distinguished (**Figure 6**). The lower (*A*) and upper (*B*) points define *h*, and the outermost left and right (pairs of from points *A*, *B*, *C*) points define *b*. These directory curve variants can be selected when designing the moldboard depending on the work performed by it. When *f* is changed in vertical position *k*, the moldboard's overall height *h*<sup>0</sup> also remains low. Parameter *δbmax = bi*�*b* obtained after formation of an edge of the surface *Φ<sup>i</sup>* edge, is located opposite to the point at which the rotation axis *k* passes (*right/left*–on the

*Variants of rotating axis (k) positions of working surface relatively to directory curve m. A, B, C – extremely*

*Application the Geometric Modeling Methods and Systems in Design Engineering…*

new working surface. As a result, an edge separating the working surface into two halves is formed on the working surface. On the basis of this model, it is possible to develop various constructive variants of transformed moldboard's design models, allowing to transform from one working surface in another. It is known that when designing complexity technical forms, the considering surface is mentally different by "*geometric*" and "*working*," since from the same surface, it is possible to obtain different working surfaces [4, 11]. Therefore, it can form new required working surface *Φ<sup>i</sup>* by proposed model, that is, by rotating working surfaces *Φ<sup>a</sup>* and *Φ<sup>b</sup>* around the axis *k* in angle *αi*. Although given *Φ* and newly formed *Φ<sup>i</sup>* surfaces are cylindrical, they have different working surfaces with different functional properties, where *α* becomes the control parameter in the formation of *Φi*. New working surface *Φ<sup>i</sup>* improves directional action of the moving layer mass on the outside (**Figure 4b**) and from the inside (**Figure 4c**) than given surface *Φ*.
