Theoretical studies of oscillations of the cleaning working bodies spiral potato separator

Abstract

Purpose. Increase of efficiency of potato tubers cleaning process from impurities of new construction of spiral separator taking into account and activation of vibrating process of its cleaning spiral springs. Methods. The research was carried out with the use of higher mathematics, theoretical mechanics, elasticity theory and methods of programming and numerical calculations with the help of PC. Results. For the developed construction of the spiral separator of potato heap, which consists of cantilever mounted cleaning spiral springs, the mathematical model of free ends of spiral oscillations under the influence of external load is developed. An equivalent bending scheme of the cantilever spiral under the action of uniformly distributed load, selected corresponding axes of coordinates and parameters characterizing the vibrational process of the spiral end are determined. For such an equivalent scheme, a differential equation of cleaning spiral oscillations in partial derivatives is made for the first time. After the corresponding transformations, the differential equation was numerically solved according to the program, by means of a PC. This made it possible to find the dependence of the change in the winding pitch of the cleaning spiral spring as a result of its deformation, in particular, the simultaneous longitudinal stretching and transverse deflection, on its length. Also new analytical dependences of the reduced moment of inertia of the section of the cantilever spring are received, on the basis of which graphic dependences of change of its value on length of a spiral spring at the set diameter, pitch of skills, angle of rise of a coil and angular speed of rotation have been received on the PC. Conclusions 1.The calculated mathematical model of vibrations of the working bodies of the spiral separator of potato heap is constructed, as a result the differential equation of transverse bending vibrations of its console cleaning spiral spring is made. 2.On the basis of the differential equation solution of transverse bending oscillations of the cleaning spiral spring the analytical expressions describing the law of vibrational process and deflection of the spiral spring at any moment of time for any point of its longitudinal axis are received. 3.Analytical dependencies are obtained to determine the variable pitch of a curved coil spring at any given time and for any inter-turn lumen during this oscillatory process. 4.At the angular velocity of the spiral spring, which is equal to ω = 30 rad∙s-1, the density of the material of which the spring is made, = 7700 kg∙m-3, modulus of elasticity Е = 2∙1011 Pa, the radius of the bar = 8.5 mm, uniformly distributed spiral spring load by potato heap intensity 1000 Н∙m-1 the total spring deflection along its length varies from 0 to 0.25 m. 5.The obtained analytical expressions of restriction on the maximum change of the cleaning spiral spring pitch at its fluctuations from the condition that potato tubers do not fall into the spring inter-turn space taking into account structural and kinematic parameters of the cleaning spiral spring, the material from which it is made, technological modes of operation and tubers' sizes. 6.As the numerical calculations on the PC show, a cleaning spiral spring with the above parameters and an initial winding pitch S = 48 mm at the considered transverse oscillations at the expense of deformation can change a step up to 54 mm that will provide not falling out of a potato tuber outside of a separator of a potato heap. Keywords: potatoes, digging, impurities, cantilever spiral spring, oscillations, differential equation, numerical calculations on PC.