Justification of the flat shaft profile using variation calculation methods

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.

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