Stability of the coupled vibrations of work roll and strip in cold rolling process

Abstract

Undesirable vibrations that occurred in cold rolling mills, widely known as chatter, are studied in this article by considering the interaction of three types of vibrations, namely, the longitudinal vibration of the rolled strip and the torsional and vertical vibrations of the upper work roll. The dynamic component of rolling force is determined using the quasi-static model under the assumption that the changes in roll gap and strip tension produce the variation of rolling force. The coupled vibrations of the work roll and rolled strip are mathematically governed by a set of 3-degree-of-freedom nonlinear equations. Under chatter conditions, a new variable is introduced to represent the motion of the quasi-neutral point. A stability criterion for the motion of the quasi-neutral point is developed by studying the eigenvalues of the corresponding characteristic equation of the linearized parts of the non-linear equations. The chatter stability can then be examined by evaluating the determinants of five matrices. Numerical examples are given to show the stable and unstable vibrations in the cold rolling process. The unstable vibration would lead to skidding phenomenon and even break the rolled strip. The results presented in this article provide new insights into the dynamic interaction of the coupled vibrations and the dynamics of the rolling process.

Instability Condition Derivation for Hydraulic AGC System under Pressure Closed‐Loop Control

“…In combination with equations ( 15), (17), and (19), when small disturbance motion happens in the system close to the operating point A, the incremental equations of the hydraulic transmission element can be derived.…”

“…Huang et al [18] investigated the effects of asymmetric structure parameters on the stability of rolling mill via the numerical approach. Ji [19] studied the chatter in cold rolling mill in view of the interaction among vertical or torsional vibrations of upper work roll and longitudinal oscillation of rolled strip. A time-varying criterion was developed to estimate the stabilization of tandem cold rolling mill by Lu et al [20].…”

Coupled Vibration Behavior of Hot Rolling Mill Rolls under Multinonlinear Effects

“…e calculation accuracy of rolling force greatly affects the distribution of friction force and strip quality in the deformation zone. Many expressions for rolling force under different working conditions have been proposed by analyzing, simplifying, and regressing the characteristics of nonlinear coupling vibration of the rolling mill and dynamic components of rolling force based on actual tests [18,20]. Of them, we adopt the Alexander-Ford formula for hot rolling [21].…”

Construction of a force method for estimating the longitudinal stability of the process of thin sheet rolling

“…Issues on the dynamic fluctuations of strip in the rolls, as well as working rolls, were examined in papers [13,14]. They suggested theoretical models that make it possible to predict these phenomena when setting up equipment for sheet rolling.…”