To calculation of the porosity grain layer on a flat vibrating sieve

Abstract

In article the graphic method of porosity determination of a moving layer of a grain compound on a plane vibrosieve which is tilted under some angle to the horizon has been described. For achievement of a goal the analytical solution of a non-linear differential equation of the second order was constructed. It has been integrated by numerical methods on the computer earlier. This decision has been presented in the form of the improper integral of the second kind with integrable singularity. The order of a degree singulyarity was equal to 1/3. Transition to the dimensionless variables received in the graphic form dependence of value of integral on value of variable upper limit of integration. The diagram which gives the chance to calculate concentration of grain particles (or specific weight) in any point on thickness of a layer of the separated grainmixture on a plane vibrosieve was constructed. For this purpose it is necessary to know only coefficients of the input differential equation which depend on parameters of oscillations of a sieve and angle of its inclination to the horizon and on physicomechanical characteristics of a grainmixture. On specific numerical examples it was illustrated rather high accuracy of the offered graphic method of calculation and good coherence of results. It results in good results of the known numerical integration of a non-linear differential equation. It is set that the offered method is suitable also for identification of parameters of a mathematical model on the measured change of concentration of grain particles on thickness of the separated grainmixture layer. The developed graphic method is rather universal and can be an alternative to the known numerical methods of calculation. The method doesn't require unwieldy computation and is rather simple in application. In case of implementation of a method it is expedient to carry the tabular form of record of results.