yet still retain the essential features of the more detailed
models. Based on this, the objectives of the work described
herein are
(1) to develop a simple model (which could be
implemented on a desktop PC) to provide some
rough indication that additional work using more
detailed models is likely to be successful, and
(2) to show how the simple model can be used when
coupled to a controller (in this case a linear
quadratic (LQ) tracking regulator with a constant
disturbance).
II. DESCRIPTION OF THE PROCESSS
In the tandem cold rolling process, metal strip is passed
through a tandem mill which consists of up to six pairs of
independently driven work rolls, with each work roll
supported by a back-up roll of larger diameter. As the strip
passes through the individual pairs of work rolls, the thickness
is successively reduced. The reduction in thickness is caused
by very high compression stress in a small region (the roll
gap) between the work rolls. In this region the metal strip is
plastically deformed, and there is a slipping between the strip
and the work roll surface. The necessary compression force is
applied to the bearings of the back-up rolls by hydraulic rams,
or by a screw arrangement driven by an electric motor. The
energy required to achieve the reduction in strip thickness
causes a temperature rise (at the roll gap), which is reduced
considerably by the cooling effects of air and rolling solution
(lubricant) as the strip travels between the stands.
Mill instrumentation generally consists of sensors to
measure roll force at each stand, interstand strip tension force,
strip thickness (at the exit of the first and last stand), work roll
speeds, and roll gap actuator (hydraulic ram or screw)
positions.
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