Mathematical modeling and design parameters of crushing machines with variable-pitch helix of the screw

From the point of view of the effectiveness of the top cutting unit, the helix angle in the end portion of the screw is the most important and characteristic parameter, as it determines the pressure of the meat material in the zone of interaction of a knife and grate. The importance of solving the problem of mathematical modeling of geometry is due to the need to address the problem of minimizing the reverse flow of the food material when injecting into the cutting zone, as the specified effect of "locking" significantly reduces the performance of the transfer process, increases energy consumption of the equipment and entails the deterioration of the quality of the raw materials output. The problem of determining the length of the helix variable pitch for screw chopper food materials has been formulated and solved by methods of differential geometry. The task of correct description of the law of changing the angle of helix inclination along its length has been defined in this case as a key to provide the required dependence of this angle tangent on the angle of the radius-vector of the circle. It has been taken into account that the reduction in the pitch of the screw in the direction of the product delivery should occur at a decreasing rate. The parametric equation of the helix has been written in the form of three functional dependencies of the corresponding cylindrical coordinates. Based on the wide range analysis and significant number of models of tops from different manufacturers the boundaries of possible changes in the angles of inclination of the helical line of the first and last turns of the screw have been identified. The auger screw length is determined mathematically in the form of an analytical relationship and both as a function of the variable angle of its rise, and as a function of the rotation angle of the radius-vector of the circle generatrix, which makes it possible to expand the design possibilities of this node. Along with this the mathematical expression has been obtained for calculating the length of the auger body necessary in the study and calculation of energy costs for the product movement processes. The developed theoretical materials are in good agreement with the experimental data available in the literature on the investigation of press and extrusion mechanisms, this will make it possible to apply them effectively in the design practice.