Elements of the Process Theory

With the method of upper-limit estimate an optimal geometry of rolled parts’ section at cross-wedge rolling is determined. The geometry supplies  minimum energy of forming. An influence of deformational metal strengthening on geometrical parameters of a blank is set.

Statistically and cinematically correct fields of slide lines are constructed numerically at cross-wedge rolling of an endless cylinder with flat slabs at a centered deformation field (with cogging rate >1.025). Strain and deformation levels in a plastic field are determined. The decisions take into account breaks of flow speed at the boundaries of hard and plastic areas.

Statistically correct fields of slide lines are constructed at little cogging rates <1.025 when deformations in the cylinder section do not penetrate into the axis, and a local field of deformational centre realizes. A variant of proportional distribution of strain at contact is examined.


A new scheme of deformed cylinder cross section geometry at cross-wedge rolling of an endless cylinder by three rollers is proposed. With the method of upper-limit estimate genuine geometry of contact and free surfaces for the proposed scheme is determined with the help of consecutive approximation of geometrical parameters of cylindrical body section. Rolling efforts are calculated; non-equiangular, statistically correct slide lines fields are constructed.

Cross rolling of a tube is considered when width of a tube side is insufficient and a plastic hinge appears in Section B-B which causes tube rigidity loss and rolling cessation. Minimal tube width is determined with the method of upper-limit estimate when plastic hinge appears and contortion begins.


A method of calculation of deformed metal cavity revelation probability is developed.  Allocation of plasticity of initial materials corresponds with Gauss’ law of normal allocation.




Plasticity resource is determined by an original experimental method of cross-wedge rolling of a flat disc which is cut out of a blank produced with cross-wedge rolling. The method allows to determine with high accuracy a part of material plastic properties spent under certain conditions of cross-wedge rolling.

Models of viscous metal destruction at plastic deformation are considered, including cross-wedge rolling. Metal and alloy deformation represents a surface in position data of shear enhancement ratio depending on the first invariant of stress tensor and on cube root of the third invariant of stress deviator. It is shown that traditionally applied plasticity diagram is a special case of a deformation surface.

Modelling of the cross rolling process was carried out with the help of the method of finite elements using the packages of engineering analysis ANSYS and LS-DYNA. Computer model of the process of cross rolling takes into account the multivariation of conditions and characteristics, depending on the boundary contact conditions, heating rate, blank material, which in their turn influence the strain state and energy-power parameters, that limit the stability of the process of cross rolling, including the opening of the axial cavity.

А multifactor model of cross-wedge rolling was created The problems of regulating the spatial development of the process of plastic forming for different technological processes of cross-wedge rolling have been solved. The worked out computer model allows to conduct the analysis taking into account different peculiarities of geometrical configuration of wedges, their dimensions, blank material and the regularities of their forming, without manufacturing the part itself. Modelling allowed to raise the effectiveness of the process by using most fully the resource of plastic properties of metals and alloys.  

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