Kinematics of the deformation zone in plugless rolling of oil pipes

This article describes the process of plugless rolling of oil pipes. Correlations between caliber parameters and swaging were obtained. The mathematical model of the process of plugless rolling of pipes was made. Main parameters of the deformation zone were determined. A set of equations to determine the surface of the contact area of the round billet and the tool for two-roll and three-roll calibers was obtained. The velocity field of metal billets was presented. From the assumption that the axial component of the velocity vector changes according to the quadratic law and the metal entrance velocity in the deformation zone is connected with the exit velocity from the deformation zone by the reduction ratio, the dependence for the determination of this component of the velocity vector was obtained. The linear function of the radial component of the velocity vector was justified. From the relation of axial and radial components of the velocity vector by the tangent of the angle between the considered section and the vertical symmetry plane of the roll a dependence for the determination of the radial component of the velocity vector was defined. The third component of the velocity vector was determined subject to the incompressibility condition, which was defined for three-roll and two-roll calibers. Based on the determined components of the velocity vector, the components of the strain velocity tensor were defined for three-roll and two-roll calibers. The components of the strain velocity tensor were calculated for the case of rolling tubes in a three-roll reduction mill. The components of the strain velocity tensor were numerically estimated, and the components of the strain velocity tensor that may be neglected in engineering calculations were determined.