The scientists of the Kharkov Petro Vasylenko National Technical University of Agriculture have created special separators of vibrations for treatment of grain mixtures in selection and preparation of seed to sowing. High quality of separation on these separators is achieved due to the simultaneous use of complex of many properties of particles: resiliency, roughness, largeness, shape. However a high-quality division of mixtures is observed when motion on workings bodies (the surfaces of friction) takes place in a single layer. Then every particle can contact with a surface and exercise its properties in a maximal degree. Thus the increase of grain feeding and productivity of such separators to the level of sieve machines is not possible. The new method of division of corn mixtures of separation on the limited area of trajectory is used in which doesn’t have these drawbacks. In addition, the fact that workings bodies of separator are produced compact and placed in greater quantity in the same volume multiplies their productivity. This effect is doubled, if the workings bodies are manufactured in the shape of a symmetric gutter with a curvilinear profile and adjusted with a reflecting plate in his middle part. Then grain feeding on every working body can be carried out in two streams.

The problem of choice of rational profile of working body is related to the study and comparison of features of motion of seed on his surface at the different form of transversal section: circumferences, parabolas, hyperbolae, and others. It causes the necessity of study of technological process of separation on the base of mathematical model of motion of seed on curvilinear surfaces. This problem is not well enough investigated in the scientific literature. This paper deals with the case when the section of working body has a shape of quadratic parabola.

Taking into consideration the forces affecting the grain, the system of differential equations of its motion is written down in the natural system of axes. The decision of this system is executed in the environment of Mathcad. Taking into account possibilities of symbols in Mathcad, the program was created for a case, when the type of working body has an arbitrary shape. To start this program it is necessary only to enter equation of the explored type as a user’s function.

The technologically justified periodic mode of motion of corn particle without tearing away and slipping was explored. In this mode the time of motion of particles on the surface of working body between two successive accents on reflector is equal to the period of vibrations of mobile part of separator. It is shown that in the case of parabolic type of working body interruption of the indicated mode is mostly possible in area of maximum remove of particles from a reflecting plate, where a normal reaction takes on a minimum value.

The criterion of separation of mixtures is a scope of fluctuating motion of particles on working bodies. Resilient particles have a greater scope than unresilient ones. In addition, distribution of the masses within a particle (ratio of radius of inertia to the radius of particle) affects the scope. It proves the possibility of separation of particles according to their mechanical properties on working bodies with a parabolic profile.

The best effect of separation for the considered mode of motion of particles on a parabolic profile can be achieved under the intensity of vibrations close to the minimum possible. At the high rates of intensity of vibrations the distinction in trajectories of motion of particles, having different features, disappears and that makes the separation of mixtures almost impossible.

Key words: small sounding board, reflecting surface, periodicity of motion, scope of vibrations of particle on the type of sounding board.