Теорія змушених поперечних коливань коренеплоду у ґрунті як у пружнодемпфуючому середовищі при вібраційному викопуваннi

Abstract

Goal. To substantiate theoretically the parameters of transverse oscillations of the root as an elastic body located in the soil as in an elastic damping medium for the case when the perturbing forces coincide with the direction of the progressive movement of the digging working body to prevent breakage of roots during vibration excavation. Methods. Theoretical research was conducted using the methods of theoretical mechanics and higher mathematics, including the theory of oscillations and calculus of variations. Numerical calculations and construction of graphical dependences were performed on a PC using compiled programs. Results. The theory of forced transverse oscillations of a root crop as an elastic body located in the soil as in an elastic damping medium during vibration excavation is developed for the case when perturbing forces are directed perpendicular to the root crop axis and coincide with the direction of the progressive movement of the excavating working body. Based on the application of the Ostrogradskyi-Hamilton variational principle using the developed equivalent scheme, analytical expressions were obtained to determine the amplitude of forced transverse oscillations of the root body depending on the amplitude of the perturbing force and the coefficients of elastic deformation and damping of the soil for any cross-section. According to the developed program, numerical calculations were performed on PC, which allowed building graphs of changes in the amplitude of forced transverse oscillations of the root as an elastic body in the soil as in an elastic damping medium, from the amplitude of the perturbing force, elastic deformation coefficients c and soil damping b. Conclusions. According to the results of calculations, ranges of values are obtained of the coefficient of elastic deformation of the soil (c = 1.0·105…1.3·105 N·m–3), for which the resonant regime is observed, i.e. the value of the amplitude of transverse forced oscillations of the elastic body of the root exceeds the allowable limits at a frequency of perturbing force equal to n = 10 Hz. At the same time, the amplitude of these oscillations can reach 0.47 m, especially at the points of the capture of the root crop and the endpoint of its body. This can lead to breakage, so such ranges of soil elasticity should be avoided. When changing the soil damping coefficient b in a fairly wide range of 0–10 (N·s2)·m–3 there is no resonant mode, and the amplitude of transverse oscillations is within acceptable limits. Therefore, the damping properties of the soil are acceptable throughout the study range. When developing excavation working bodies with the considered direction of oscillations, it is necessary to take into account the elastic properties of the soil, where such working bodies can work effectively. The results of the analytical research were used to develop a new design of the vibrating excavation working body.