Non-circular arc temper rolling model considering radial and circumferential work roll displacements

The thesis considers the development of a non-circular arc rolling model for the calculation of the force and power requirements for temper and skin-pass rolling of cold rolled strip. This model serves for the dimensioning of temper rolling mills as well as for the calculation of preset values in process control computers. A main contribution of this work is represented by the fact that the model takes into account not only the radial but also the circumferential displacements of the work roll surface. The calculation of the surface displacements is based on a semi-analytical procedure using a numerical superposition of influence functions. This approach ensures an improved modeling of temper rolling, as the circumferential work roll displacements in combination with a modified Coulomb friction law allow for the existence of a slip- as well as a no-slip-zone. The model is based on Karman’s theory but extended including additionally an elastic compression zone at roll gap entry, an elastic recovery zone at roll gap exit and possible plastic zones in between, whereby elastic regions (internal elastic zones) are also allowed to arise between plastic zones. The numerical algorithm ensures the self-adjustment of the boundaries between elastic and plastic zones. Consequently, another important advance of this thesis is that the rolling model detects the appearance of „contained plastic flow“ automatically without using additional simplifying assumptions. The model uses an adapted rate-dependent elasto-plastic constitutive law. The re-calculated speed exponent, who primarily expresses the rate-dependence in the model, is in very good agreement with results from high-speed tensile tests of the strip material with variable strain rate. The developed model represents a physically based and mechanically consistent model with robust numerical algorithms. Excellent agreement between measured and predicted rolling forces and rolling torques was achieved.