Stability Analysis of Chatter in Tandem Rolling Mills—Part 1: Single- and Multi-Stand Negative Damping Effect

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Huyue Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
State Space ◽  
Process Model ◽  
Structural Model ◽  
Rolling Process ◽  
Space Representation ◽  
Mathematical Form ◽  
Stability Criteria ◽  
Model Stability ◽  
State Space Representation ◽  
Negative Damping

Many different modes of chatter in rolling and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been fully established and accepted. In this two-part paper, stability of tandem mills is investigated. In Part 1, state-space models of single- and multi-stand chatter are formulated in a rigorous and comprehensive mathematical form. Then, the stability of the rolling system is investigated in the sense of the single- and multi-stand negative damping effects. First, a single-stand chatter model in state-space representation is proposed by coupling a dynamic rolling process model with a structural model for the mill stand. Subsequently, a multi-stand chatter model is developed by incorporating the inter-stand tension variations and the time delay effect of the strip transportation based on the single-stand chatter model. Stability criteria are proposed and stability analyses are performed to create corresponding stability charts in terms of the single- and multi-stand negative damping mechanism through numerical simulations. Particularly, the effect of friction conditions on chatter is examined and an explanation is given for the existence of an optimum friction condition. In Part 2, the regenerative effect and resulting instabilities are examined. Suitable stability criteria for each mechanism are established and stability charts are demonstrated in terms of relevant rolling process parameters.

Single- and Multi-Stand Chatter Models in Tandem Rolling Mills

2008 ◽  
Author(s):  
Huyue Zhao ◽  
F. Ehmann Kornel
Keyword(s):  
Stability Analysis ◽  
State Space ◽  
Process Model ◽  
Structural Model ◽  
Work Roll ◽  
Rolling Process ◽  
Complete Analysis ◽  
Space Representation ◽  
Mathematical Form ◽  
State Space Representation

Many different modes of chatter and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been established. One of the most important reasons for this can be attributed to the fact that only oversimplified models with a single input and a single output were historically used to formulate chatter in rolling. Such a situation has hindered a complete analysis of the underlying mechanisms. In this paper, a state-space representation of single- and multi-stand chatter models will be proposed in a rigorous and comprehensive mathematical form for stability analysis of the various chatter mechanisms. First, a dynamic model of the rolling process that utilizes homogeneous deformation theory will be established that includes the material strain-hardening and work roll flattening effects. By coupling this dynamic rolling process model with a structural model for mill stands, a single-stand chatter model in a state-space representation will be proposed. Based on the single-stand chatter model, a multi-stand chatter model will be formulated by incorporating the inter-stand tension variations and the time delay effect of the strip transportation. A simulation program will also be presented for the study of the dynamic rolling process in the time domain and for verifying the results from stability analysis.

Regenerative Chatter in High-Speed Tandem Rolling Mills

2006 ◽  
Author(s):  
Huyue Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Mode Coupling ◽  
High Speed ◽  
Process Model ◽  
Structural Model ◽  
Rolling Process ◽  
Space Representation ◽  
Regenerative Chatter ◽  
State Space Representation ◽  
Negative Damping ◽  
Delay Differential

Third-octave-mode chatter, the most detrimental form of rolling chatter, is generated by means of negative damping, mode coupling, and regeneration. While mechanisms that include negative damping, and mode coupling have been thoroughly investigated, those associated with the regenerative effect remain elusive. In this paper, the mechanisms that may lead to regenerative chatter are studied through a state-space representation of a multi-stand mill that is constructed by coupling a homogenous dynamic rolling process model with a structural model for the mill stands in a high-speed tandem mill configuration. Stability analysis, by using the integral criterion for the stability of systems described by delay differential equations, is carried out for the regenerative mechanism in order to better understand the effects of rolling parameters on a single stand as well as the overall system. Preliminary simulation results, based on the proposed chatter model, are presented to demonstrate the feasibility and the accuracy of the chatter model, as well as to investigate chatter phenomena too complex to be studied analytically.

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