Application of hyperbolic sine velocity field for the analysis of tandem cold rolling

• Hyperbolic sine velocity field is proposed in tandem cold rolling.
• Analytical solutions are established based on elastic and plastic mechanics.
• The calculated results can be used to analyze the cold rolling process.
• The effects of ε, m  , σbσb and σfσf on xn/l and nσ are discussed respectively.

Automatic control systems for tandem cold rolling are constantly being applied due to consumers’ requirements: good flatness and surface finish, accurate strip thickness, and consistent metallurgical properties. And those requirements are related to accurate prediction of the roll force directly. A novel analytical approach to predict roll force in tandem cold rolling is proposed based on elastic and plastic mechanics. A hyperbolic sine velocity field is firstly proposed to get the required minimum roll force in plastic deformation zone in this paper. The field, Inscribed Dodecagon (ID) yield criterion and the co-line vector inner product method are applied to integrate the analytical expression of total deformation power functional. The values of roll torque, roll force and stress effective factor are obtained considering the effect of roll flattening on the roll force. A good agreement between theoretical predictions of roll force and other researchers’ models, especially on-line measured roll force in a tandem cold rolling plant, verifies that the proposed mathematical model is efficient and stable, and the model can be considered to be applied in cold rolling. Besides, the effects of rolling parameters on location of neutral point and stress effective factor are discussed respectively.