The process of strip rolling is analyzed by the upper bound technique
and presented through a software package. The effect of the input parameters,
such as reduction, relative strip thickness, friction, and front and back
tension, on the process dependent parameters, such as torque, roll pressure,
forward slip, etc., is presented quantitatively by explicit expressions.
These expressions are treated by a user-friendly software package that
presents the results in tabular and graphical forms. Also studied are the
effects of process input parameters on maximum possible reduction, alligatoring,
and the development of internal cracking (central burst).
Three different flow patterns are treated, one continuous deformation
field and two multi-triangular fields. The multi-triangular velocity field
divides the deformation region into a number of rigid triangles, separated
by surfaces of velocity discontinuity. The rigid triangles move either
as rigid bodies in linear motion, or in a more universal rotational motion.
The rigid body linear motion is just a special case of the rotational motion.
However, the linear motion is easier to treat and faster to execute. When
these solutions are compared they are found to agree with each other, support
one another and lend confidence in their reliability. Because the solutions
are presented in an explicit form they are simple to implement on an IBM
PC, and their execution is fast.
This paper focuses on the implementation of the results of the analysis
in a PC software package for process design. The effects of each of the
major input parameters on performance provides the tools for the selection
of optimal operation. For example, the determination of the range of processing
parameters that lead to the defect of alligatoring, provide a tool to prevent
Another example is the determination of the "Minimum required friction"
to prevent skidding, where the strip stalls and the rolls skid over it.
Here the analysis, when executed by the software package, provides the
characteristics of the forward slip as a function of friction. As friction
reduces, so does the forward slip, and the position of the neutral point
gets closer to the exit. The value of friction at which forward slip diminishes,
the neutral point approaches the exit, and skidding commences, is the "minimum
Key Words: Strip Rolling, Upper Bound Approach, PC