Formation a strip with a trapezoidal cross-section into a ring by rolling between conical rolls

The formation of helical surfaces requires a ring that enables their continuous production without welded seams. The aim of this study was to develop an analytical description of the process of deforming a straight strip into a ring as a result of rolling it between conical rolls. The research methodology was based on analytical modelling of the process of plastic deformation of the strip using assumptions about the isotropy of the material and the constancy of its volume. As a result of the study, analytical dependencies were obtained between the dimensions of the strip cross-section before rolling and the parameters of the ring after rolling, which allow determining the optimal geometric characteristics for forming rings of a given radius. Generalised analytical expressions were developed to determine the elongation coefficient and ring radius, which take into account the change in the aspect ratio of the trapezoidal cross-section of the strip. A model of step-by-step rolling has been proposed, which describes the gradual reduction of the aspect ratio of the trapezoidal cross-section to a rectangular one, ensuring a uniform cross-section of the ring. The obtained expressions made it possible to solve both direct and inverse problems, determine the parameters of the initial strip for forming rings of different radii, predict the geometry of the ring based on the known dimensions of the strip, and use the obtained data to adjust the rolls before experimental verification. The proposed model of step-by-step rolling ensured a uniform cross-section of the ring, which increases the accuracy of manufacturing screw surfaces without welded seams. The results may be applied in mechanical engineering for the production of screws, helical surfaces, and conveyors without welded seams, particularly in the agricultural, food-processing, construction, and energy industries