*2.3.3 Parameters of designed working surface's formative lines*

Criteria for choosing the variants of the characteristic points of the directory curve *m* by *h* and *b*, in the design of the moldboards can be explained by linking these points to the characteristic positions of the formative lines *l*. For example, we distinguish the following positions of the formative lines *l*, passing through characteristic points *m* in width *b* with respect to *h*: upper, lower, frontal, rear, and middle (by *h* or *b*), and determine their influence on the nature of the movement of the layer mass on the working surface of the moldboard (**Table 3**). It follows from **Table 3** that the nature of the layer mass movement along the working surface can be controlled by changing the relationship *h* and *b*, by changing angle *β* of the *k*-axis inclination. In contrast to vertical position, the inclination *k* at angle *β* forwards or backwards gives the working surface, in addition to improving the shift of the transported mass to the side when it is horizontally leveled (**Figure 7a**), also improves the functional properties of the inclined slopes (**Figure 7b**) and lifts (**Figure 7c**) from the transported mass. This is achieved by changing the positions of formative lines *l*, which also represent the plowshares, relative to the horizontal plane by angle *φ*, after formation *Φi*. The angle *φ* can be determined by the projection model based on the principles of descriptive geometry [16], superimposing horizontal plane with frontal, by rotating it in 90°, on the front projection we combine projections *k* and *l* (**Figure 7d**). Rotate *l* by the angle *αi*, marking with *l* 0 , and easily find the front projection *lv* 0 . Since *l* rotates on a frontal projection plane perpendicular to *k*, the rotation circle *l* is projected on a horizontal plane as an ellipse. Using the projecting rays, we find *lh* <sup>0</sup> and determine the *φ*—the angle of

inclination *l* to the horizontal plane by the rectangular triangle method, also considered as the angle of inclination to the plowshare. After transformation of the working surface *Φ* by *Φ<sup>i</sup>* with inclined *k*, the overall height of the blade *h*<sup>0</sup> increases, although *h* decreases by *δh*. The upper part of the ridge tilts forward or backward

*Developing the construction of moldboard with bilateral action working surface. a) for outside action; b) for*

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

working surface, the lengths of corresponding *li* formatives change within the range of *0 < δb < δbmax*, displacing the ends of the surfaces forming the ribs, change. At the point at which the axis of rotation *k* passes, the length of *li* is equal to *δb=0* and

The definable parameters of *Φ<sup>i</sup>* has two variants, on base of descriptive geometry principles, make sure that under alike *α<sup>i</sup>* parameters *Φ<sup>i</sup>* is also alike, but mutually negative (**Figure 8a, b**) [16]. This allow to combine two variants in one construction, which will enlarge the functional possibilities of designed moldboard (**Figure 8c**). It will select five compartments of working surfaces on intersection lines. Alternate switching-on or switching-off corresponding compartments will enable to work moldboard in three modes: moving the layer mass frontal, outside, and inside. The proposed geometric model of transformed working surface allows to development multifunctional moldboard. This development is intended for designing organization to production of specific machines. Parameterization of moldboard's working surface relieves designer's work, increases choosing variants under development moldboard's

The author developed a geometric model for giving directory curve of working surface and implemented in *AutoCAD 2012* and *SIMPLEX* systems. It was found that *SIMPLEX* system has some advantage over *AutoCAD* in solving constructive geometric modeling problems [17]. Unlike *AutoCAD*, where the giving process of directory curve automated only for ellipse and circles, in *SIMPLEX* process of giving automated for any conics and Bezier curves, by the same conditions. In addition, unlike the dynamic block developed in *AutoCAD*, the dynamic model in *SIMPLEX* will not only automate the process of changing the curve parameters, but also the process of determining the projection of the guide in a different position for cylindrical surface, and in case of a cylindroidal surface will determine them as

the nose (upper or lower) part of it is equal to *0 < δb < δbmax*.

working surface, and allows effectively solve the constructive problems.

**2.5 Dynamic model of working surface's directory curve**

template lines in each section.

**219**

. As a result of the transformation of the

relative to the lower part, shifting by *δb*<sup>0</sup>

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

*inside action; c) sections of working surface.*

**Figure 8.**

**2.4 Sections of designed working surface**


#### **Table 3.**

*Formatives' positions and their influence to working surface nature.*

#### **Figure 7.**

*Determining the geometric parameters of inclined working surface. Working surface positions: a) vertically; b) inclined to forward; c) inclined to back; d) geometric model for determining parameters.*

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

**Figure 8.**

0 ,

. Since *l* rotates on a frontal projection plane

postponed in before.

postponed in before.

Not available Average–*С* Completely taken on breast and

<sup>0</sup> and determine the *φ*—the angle of

**mass on worker of the surfaces**

powerfully postponed in before.

*2.3.3 Parameters of designed working surface's formative lines*

*Design and Manufacturing*

and easily find the front projection *lv*

3 Superior/

**Table 3.**

**Figure 7.**

**218**

Interior–*В*/*А*

ellipse. Using the projecting rays, we find *lh*

**Anterior Average Posterior**

*Formatives' positions and their influence to working surface nature.*

Criteria for choosing the variants of the characteristic points of the directory curve *m* by *h* and *b*, in the design of the moldboards can be explained by linking these points to the characteristic positions of the formative lines *l*. For example, we distinguish the following positions of the formative lines *l*, passing through characteristic points *m* in width *b* with respect to *h*: upper, lower, frontal, rear, and middle (by *h* or *b*), and determine their influence on the nature of the movement of the layer mass on the working surface of the moldboard (**Table 3**). It follows from **Table 3** that the nature of the layer mass movement along the working surface can be controlled by changing the relationship *h* and *b*, by changing angle *β* of the *k*-axis inclination. In contrast to vertical position, the inclination *k* at angle *β* forwards or backwards gives the working surface, in addition to improving the shift of the transported mass to the side when it is horizontally leveled (**Figure 7a**), also improves the functional properties of the inclined slopes (**Figure 7b**) and lifts (**Figure 7c**) from the transported mass. This is achieved by changing the positions of formative lines *l*, which also represent the plowshares, relative to the horizontal plane by angle *φ*, after formation *Φi*. The angle *φ* can be determined by the projection model based on the principles of descriptive geometry [16], superimposing horizontal plane with frontal, by rotating it in 90°, on the front projection we combine projections *k* and *l* (**Figure 7d**). Rotate *l* by the angle *αi*, marking with *l*

0

perpendicular to *k*, the rotation circle *l* is projected on a horizontal plane as an

1 Superior–*В* Not available Interior–*А* Powerfully postponed in before. 2 Superior–*В* Interior–*А* Average–*С* Partly is taken on breast and powerfully

**No. On width** *b***, in respect of** *h* **and through points Nature of the moving the moveable**

4 Interior–*А* Superior–*В* Average–*С* Completely taken on breast and weakly

*Determining the geometric parameters of inclined working surface. Working surface positions: a) vertically; b)*

*inclined to forward; c) inclined to back; d) geometric model for determining parameters.*

5 Interior–*А* Not available Superior–*В* Completely taken on bosom.

*Developing the construction of moldboard with bilateral action working surface. a) for outside action; b) for inside action; c) sections of working surface.*

inclination *l* to the horizontal plane by the rectangular triangle method, also considered as the angle of inclination to the plowshare. After transformation of the working surface *Φ* by *Φ<sup>i</sup>* with inclined *k*, the overall height of the blade *h*<sup>0</sup> increases, although *h* decreases by *δh*. The upper part of the ridge tilts forward or backward relative to the lower part, shifting by *δb*<sup>0</sup> . As a result of the transformation of the working surface, the lengths of corresponding *li* formatives change within the range of *0 < δb < δbmax*, displacing the ends of the surfaces forming the ribs, change. At the point at which the axis of rotation *k* passes, the length of *li* is equal to *δb=0* and the nose (upper or lower) part of it is equal to *0 < δb < δbmax*.

## **2.4 Sections of designed working surface**

The definable parameters of *Φ<sup>i</sup>* has two variants, on base of descriptive geometry principles, make sure that under alike *α<sup>i</sup>* parameters *Φ<sup>i</sup>* is also alike, but mutually negative (**Figure 8a, b**) [16]. This allow to combine two variants in one construction, which will enlarge the functional possibilities of designed moldboard (**Figure 8c**). It will select five compartments of working surfaces on intersection lines. Alternate switching-on or switching-off corresponding compartments will enable to work moldboard in three modes: moving the layer mass frontal, outside, and inside. The proposed geometric model of transformed working surface allows to development multifunctional moldboard. This development is intended for designing organization to production of specific machines. Parameterization of moldboard's working surface relieves designer's work, increases choosing variants under development moldboard's working surface, and allows effectively solve the constructive problems.

#### **2.5 Dynamic model of working surface's directory curve**

The author developed a geometric model for giving directory curve of working surface and implemented in *AutoCAD 2012* and *SIMPLEX* systems. It was found that *SIMPLEX* system has some advantage over *AutoCAD* in solving constructive geometric modeling problems [17]. Unlike *AutoCAD*, where the giving process of directory curve automated only for ellipse and circles, in *SIMPLEX* process of giving automated for any conics and Bezier curves, by the same conditions. In addition, unlike the dynamic block developed in *AutoCAD*, the dynamic model in *SIMPLEX* will not only automate the process of changing the curve parameters, but also the process of determining the projection of the guide in a different position for cylindrical surface, and in case of a cylindroidal surface will determine them as template lines in each section.

project is application of research results on geometric modeling of plow's moldboard and its surface, for their further adaptation into manufacturing. Therefore, one of final results of research is the development of design-project of plug's moldboard, prepared on the basis of developed geometric models, algorithms, and methods by non-traditional design. It can highlight the following stages of design-project:

1.Analysis, evaluation, and model selection for design-project;

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

2.Development of the concepts and models for design-project;

6.Patenting design-project for manufacturing by design conditions; and

As an example, let us take a look at the design-project of plow's moldboard. At it is known, plows used in agricultural production have different design models of their moldboards according to their purpose. Each design models has its own advantage, the isomorphic application of which in another design can lead to some loss of perfection of this design. In such cases, it is possible to combine the advantages of considered models, according to various evaluation criteria, into one new

7.Adaptation design-project for manufacturing by design conditions.

design, with the necessary changes, on one of basis methods of industrial

Moldboards have a complicated technical form, centuries-old changes to improve their designs and have a universal geometric model. These factors allow the application industrial design in the development of moldboard by geometric characteristics that affect to their technical/technological characteristics. Let us

Classic plows, having a one side turnover moldboard with cylindroidal working surface, have common use in agricultural production. Therefore, they will be considered as basic model, as it is chosen by experts as basis for development of other moldboards' design. They have good crumbling and turning indices, but these advantages are opposed to their shortcomings, which led to three improvement direction. Firstly, low manufacturability of such cases with non-sweep working surface led to development geometrically combined working surfaces [10]. Secondly, use of one side turning moldboard will lead to formation of furrows and ridges, that is, roughness of plow, which led to development vertical reversible plow. They differ in higher productivity and quality of performed works which are not demanding additional presuming agro technical actions after their using. But presence of double (right and left turning) moldboard makes construction more expensive, more metal quantity, and with greater traction resistance, which is its drawbacks, in contrast to its advantages [10]. This led to improvement in the third direction, that is, to development horizontal turn plows. There has development of technological scheme of plow with opportunities working in two right and left side, but with cylindrical working surface, which does not provide a satisfactory layer turnover [14, 21]. This analysis shows that the main reason for improvement and crossing point of advantages and disadvantages of considered designs is geometry of

3.Preparation description and sketch of proposed design;

4.Geometric modeling of the proposed design;

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

5.Computer simulation of the proposed design;

consider directions of plow's moldboard improvement.

design–"*Concept selection*" [2, 20].

moldboard's working surface.

**221**

#### **Figure 9.** *Bezier curve by forward given conditions (a) and determining it's projections by multiple agreement points (b).*

The plane of curve is vertical and at an angle *γ<sup>0</sup>* to the axis *OX*, as to the wall of the furrow. The horizontal projection of curve defines as a segment, equal to the length of *L*. Aligning the curve plane with horizontal plane, gives natural dimensions of curve in the plan. For easy control of curve, it can be set even by two Bezier curves. In this case, the tangent to the intermediate point *P4*, is tangential simultaneously to the two Bezier curves *Р1Р2Р3Р<sup>4</sup>* and *Р4Р5Р6Р<sup>7</sup>* (**Figure 9a**). Determine the position of points *P1, P4,* and *P7* on the horizontal projection. Determine the frontal projections of these points by *interactive incidence* at surface formatives' heights *h0, hi,* and *hmax*. To determine the frontal projection, use the possibility of the system "*belonging to the point of the curve in multiple agreement*". In this case, this alignment can be set on a horizontal projection or on a projection in the plan. Next, the projection links determine the frontal projection (**Figure 9b**).
