Basic Assumptions and Definitions

The following terms shall be defined:

Rolling Direction, Length Direction, Longitudinal Direction

Direction of principal material flow.

Length, \(l\)

Extent of the workpiece in rolling direction.

Thickness Direction, Height Direction

Direction of reduction during a roll pass.

Thickness, Height, \(h\)

Extent of the workpiece cross-section in thickness resp. height direction.

Width Direction

Direction of spreading during a roll pass.

Width, \(w\)

Extent of the workpiece in width direction.

Common Orientation, Usual Orientation

For profiles originating from two-roll passes the usual orientation is, that the roll gap is aligned horizontally, as shown in Figure Directions in Two-Roll Passes.

For profiles originating from three-roll passes the usual orientation is, the vertical roll gap is/was above the profile, as shown in Figure Dimensions of Three-Roll Passes.

See the following figures for clarification of height and width directions in two-roll and three-roll passes. Note, that in three-roll passes the measure width and height a rather imaginary measures, since in fact only the half width and half height can be measured, due to the 3-fold rotation symmetry.

Two-Roll Pass Directions

Directions in Two-Roll Passes

Three-Roll Pass Directions

Directions in Three-Roll Passes

In the following some basic assumptions that are made within code and design are listed. Keep them in mind while reading through the documentation. These assumptions may change in future versions of the framework.

  1. Coordinate System The \(x\)-axis equals the rolling direction, while \(y\) equals the thickness direction, and \(z\) equals the width direction. The coordinate system is right-handed.

  2. Symmetry Roll passes, profiles, and grooves are symmetric at the \(y\) axis. Despite defining asymmetric passes is possible to some extent, you should avoid this, as it may lead to wrong results. This is intended to be broken up in future releases. Symmetry along the \(z\) is not required.

  3. Stationarity Only stationary processes are calculated. There are no intrinsic dynamics within the models.

  4. SI-Units Everywhere basic SI-units are used, without scaling factors (milli, kilo, etc.). Denote orders of magnitude by using the 1.234e3 syntax of Python float literals. Especially imperial units are not supported. Principally, also other coherent unit systems may be used, but for the purpose of material databases and similar the use of basic SI is strongly recommended. Use other units at your own risk.