*2.3.1 Giving the axis of rotation of the working surface*

The process of formation of the required working surface *Φ<sup>i</sup>* can be controlled, besides the parameter *α*, also the position *k*. In the model under consideration, position of rotation axis *k* is vertical and has a certain distance relative to *Φi*. However, change in the position of *k* significantly affects the formation of *Φi*. Here we can consider two parameters of *k*: the change in the distance *f* defined between fixed points *k* and *m*, for example, the base of *k* and sock *m* on a horizontal plane; and the change in the angle of inclination *β* to the horizontal plane. At the same angle *α<sup>i</sup>* and shape of the directory curve *mi*, changing *f* will lead to change in the relative position of pairs of directory curve *m<sup>i</sup>* and *m<sup>i</sup>* 0 , which will lead to a change in the design parameters of moldboard's working surface *Φi*. Among the options (**Figure 5**) considered by the author, the variants b) chord *AB* and d) tangent in point *C* are selected as acceptable for this problem, when it will be possible to neglect parameter *f*, that simplifies the problem. Though other variants also have such working surface, it they can lead to complication of moldboard's constructive parameters. However, when the surface *Φ<sup>i</sup>* is formed, in the variant *d* rotation is performed in the opposite direction than in variant *b*. The rotation angle *α* is selected with *0 < α < αmax*, provided that the *P<sup>i</sup>* and *P<sup>i</sup>* <sup>0</sup> planes must intersect all formative lines of surfaces *Φi*, where *αmax* is equal to *tgα = (l/2)/b*, and *b*–extension of directory curve.

*Application the Geometric Modeling Methods and Systems in Design Engineering… DOI: http://dx.doi.org/10.5772/intechopen.89974*

**Figure 5.**

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

*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.*

The process of formation of the required working surface *Φ<sup>i</sup>* can be controlled, besides the parameter *α*, also the position *k*. In the model under consideration, position of rotation axis *k* is vertical and has a certain distance relative to *Φi*. However, change in the position of *k* significantly affects the formation of *Φi*. Here we can consider two parameters of *k*: the change in the distance *f* defined between fixed points *k* and *m*, for example, the base of *k* and sock *m* on a horizontal plane; and the change in the angle of inclination *β* to the horizontal plane. At the same angle *α<sup>i</sup>* and shape of the directory curve *mi*, changing *f* will lead to change in the

in the design parameters of moldboard's working surface *Φi*. Among the options (**Figure 5**) considered by the author, the variants b) chord *AB* and d) tangent in point *C* are selected as acceptable for this problem, when it will be possible to neglect parameter *f*, that simplifies the problem. Though other variants also have such working surface, it they can lead to complication of moldboard's constructive parameters. However, when the surface *Φ<sup>i</sup>* is formed, in the variant *d* rotation is performed in the opposite direction than in variant *b*. The rotation angle *α* is

formative lines of surfaces *Φi*, where *αmax* is equal to *tgα = (l/2)/b*, and *b*–extension

0

, which will lead to a change

<sup>0</sup> planes must intersect all

(**Figure 4b**) and from the inside (**Figure 4c**) than given surface *Φ*.

**2.3 Geometric parameterization of moldboard's surface**

*2.3.1 Giving the axis of rotation of the working surface*

relative position of pairs of directory curve *m<sup>i</sup>* and *m<sup>i</sup>*

selected with *0 < α < αmax*, provided that the *P<sup>i</sup>* and *P<sup>i</sup>*

of directory curve.

**216**

**Figure 4.**

*Design and Manufacturing*

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

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

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 chest or *upper/lower*–on the toe).

**Figure 6.** *Variants of relative positions of directory curve and it's constructive parameters.*
