Abstract
Using the method of calculus of variations, the task was set to determine the shape of the paw profile of a plane-cutting cultivator with minimal traction resistance. Based on this functional, the Ritz differential equation was compiled, which makes it possible to find the value of the functional by possible linear combinations of selected functions with constant coefficients composed of the first terms of the sequence, as a result of which an expression describing the required profile of the working organ was obtained. The Ritz differential equation made it possible to determine a family of extremals for a given functional: the desired curve belongs to this family and satisfies the boundary conditions of the problem. Using the finite element method, the three-dimensional problem of substantiating the profile of the tillage working body was solved. As the results of experimental studies have shown, a working organ with a reasonable profile has a lower energy consumption by 15-35% compared to traditional ones, while reducing the ridge of the soil surface along the width of the treatment.
Highlights
Creation of new and modernization of existing tillage machines and implements requires substantiation of the basic design and technological parameters
Using the method of calculus of variations, the task was set to determine the shape of the paw profile of a plane-cutting cultivator with minimal traction resistance
The Ritz differential equation was compiled, which makes it possible to find the value of the functional by possible linear combinations of selected functions with constant coefficients composed of the first terms of the sequence, as a result of which an expression describing the required profile of the working organ was obtained
Summary
Creation of new and modernization of existing tillage machines and implements requires substantiation of the basic design and technological parameters. To substantiate the rational profiles of tillage working bodies, as one of the most influencing factors on the quality and energy intensity of soil cultivation, experimental and graphic-analytical methods, principles of the theories of loose media, continuous media, plastic fluidity, and others are used. The use of such methods requires a lot of labor and does not always allow obtaining profiles close to optimal [7, 8, 9]. Purpose of the study Substantiation of the profile of the flat-cutting paw of a production cultivator with the provision of high-quality performance indicators from an energy point of view, and the preservation of the coordinates of its boundary points
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