Abstract
This study’s object is the stressed state of the plastic deformation site under conditions of load asymmetry when metal is gripped by rolls, under the determining modes of process stability. The task addressed is the implementation of shape change at the rolling process stability threshold related to a decreased force load under the increased strain impact. A physical and mathematical model of a flat rolling theory problem has been built under conditions of multi-parameter factors affecting the gripping capacity of rolls and the stability of rolling process. The plasticity theory problem was solved analytically using the method of argument of a function of a complex variable. The solution to the plane problem is shown, using the asymmetry of the process, the counter-directed flow of metal. The nonlinearity of the plasticity theory problem was taken into account. Based on the mathematical model, a new force factor was identified and investigated: the force stretching factor from the lagging zone. A new single-zone deformation mode with minimum process stability was identified. The process was investigated under conditions of multiparameter influence on rolls gripping ability and its stability. The zones of reachability were established for a deformation focus shape factor within the range of 5.00...15.00. The mode of partial suppression of the zeroing factors of the metal stressed state was investigated under conditions of multi-parameter influence on the gripping ability of the rolls and the stability of the process. Stability indicators of transient modes were determined: at α = 0.077, the ratio f/α = 1.10…1.95; at α = 0.129, the ratio f/α = 1.19…1.95; at α = 0.168, the ratio f/α = 1.28…1.95. This study’s results make it possible to solve technological problem related to the development of rolling schemes when the gripping force of friction and the pushing force of normal pressure arise during the forming process