Title

CHARACTERIZATION OF THE RESTRICTIONS IN SHAPE ADJUSTMENT CAPABILITIES ASSOCIATED WITH ACTUATOR CONSTRAINTS

CHARACTERIZATION OF THE RESTRICTIONS IN SHAPE ADJUSTMENT CAPABILITIES ASSOCIATED WITH ACTUATOR CONSTRAINTS

Authorship

Zipf, Mark E.

Zipf, Mark E.

I am this author

DOI

10.5151/2594-5297-20528

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Abstract

The shape actuators of 20-high cluster mills (top crown eccentrics and laterally traversing, tapered 1st intermediate rolls) have specific physical and operational constraints (step, bending, penetration depth limits, etc.) that diminish their ability to produce/ deliver the desired shape adjustments. These limitations can be viewed as restrictions or bounds on the set of desired shape targets that the mill can achieve. The behavior of the shape actuators can be characterized with influence functions (spatial waveforms). Using orthogonal polynomials as a basis set, these functions are described by a distribution/ spectra of spatial curvatures. The actuation constraints form bounding envelopes on the distribution/ spectra, which indicates the shape adjustments that the mill can and cannot provide. This paper examines and defines the curvature distribution bounding envelopes for the cluster mill’s top crown eccentric shape actuators for the classical “step limit” constraints. It is shown that these shape corrections capabilities envelopes are also functions of the material geometry, yield stress and reduction scheduling of the mill. Further, the nature of the roll cluster set-up and backing assembly BC actuation shafts (solid, flexible, segmented idler roll) are examined to determine their impact on these envelopes.

The shape actuators of 20-high cluster mills (top crown eccentrics and laterally traversing, tapered 1st intermediate rolls) have specific physical and operational constraints (step, bending, penetration depth limits, etc.) that diminish their ability to produce/ deliver the desired shape adjustments. These limitations can be viewed as restrictions or bounds on the set of desired shape targets that the mill can achieve. The behavior of the shape actuators can be characterized with influence functions (spatial waveforms). Using orthogonal polynomials as a basis set, these functions are described by a distribution/ spectra of spatial curvatures. The actuation constraints form bounding envelopes on the distribution/ spectra, which indicates the shape adjustments that the mill can and cannot provide. This paper examines and defines the curvature distribution bounding envelopes for the cluster mill’s top crown eccentric shape actuators for the classical “step limit” constraints. It is shown that these shape corrections capabilities envelopes are also functions of the material geometry, yield stress and reduction scheduling of the mill. Further, the nature of the roll cluster set-up and backing assembly BC actuation shafts (solid, flexible, segmented idler roll) are examined to determine their impact on these envelopes.

Keywords

20-high cluster mills; Shape actuators; Actuator constraints; Bounding envelopes.

20-high cluster mills; Shape actuators; Actuator constraints; Bounding envelopes.