VARIANT SHAPING OF WORKING SURFACES OF SOIL CULTIVATING DISCS USING VECTOR RATIONAL PARAMETRIC CURVES OF THE SECOND DEGREE

Abstract

The current stage of development of our state is characterized by difficult trials associated with military operations on its territory. Nowadays, in addition to the primary military needs, the tasks of preserving and developing the Ukrainian economy are very important. In the above circumstances, one of its basic components is agriculture. Therefore, increasing the efficiency of its production is a relevant scientific and applied problem. The successful resolution of these issues is facilitated by the further improvement of appropriate technical means, among which a leading place is occupied, in particular, by a variety of soil-cultivating implements. Currently, disc tools are considered the most progressive among them, since they fully meet existing environmental requirements and provide high energy efficiency. The presented facts determined the working surfaces of agricultural soil-cultivating discs as the subject of following studies. Rational curves of the second degree in vector parametric form were chosen as the mathematical basis for their modelling, due to certain useful properties of these lines. This refers to the clarity and predictability of shaping, a simple analytical apparatus, and adaptability to the implementation by computer geometric means of automated design systems. At the same time, the main goal is not only to cover the existing working surfaces of agricultural discs, but also to expand their range in order to improve the design and operational parameters and characteristics, the manufacturing processes of these products. A generalized mathematical model is proposed, which contributes to increasing the productivity of computer variant processing of the considered technical objects, conducting their complex multi-criteria optimization taking into account various requirements. For example, this applies to strength, design, reliability, manufacturing technology, operation, economics, etc. This is due to the unifying integrating role of geometric models for other mathematical descriptions of industrial products. This publication also presents some directions for applying the obtained results in areas of life other than agriculture.