Among various types of rolling chatter, third-octave-mode chatter is considered the most critical because it generates large gauge variations in the rolled materials and may damage the rolling mill. In this three-part paper, a new chatter model that combines a homogeneous process model with suitable mill structure models is presented. Based on this model, the system's stability is investigated in the light of various mechanisms that may lead to the onset of third-octave-mode chatter. Stability criteria for each mechanism are established in terms of relevant rolling process parameters, and their influences on overall system stability are demonstrated. Part 1 deals with the general formulation of single- and multiple-stand chatter models.
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. IntroductionThird-octave-mode chatter, usually occurring in the range of the third musical octave between 128 and 258 Hz [1], is considered the most significant and detrimental among rolling chatter types since it leads to large gauge variations of the rolled strips and may damage the mill stands. As pointed out in various studies [2][3][4][5][6][7][8], third-octave-mode chatter can be incited by different mechanisms such as model matching, negative damping, and regeneration. Although these mechanisms have been identified after years of research, no clear and definite theory of their mechanics has emerged. One of the important factors responsible for this situation is the fact that either oversimplified single-input single-output (SISO) [1,2,5] or complex multiple-input multiple-output (MIMO) chatter models [3,4,6] were historically used to formulate chatter in rolling. The oversimplified SISO models were targeted for single-stand conditions only and thus prevented the understanding of chatter mechanisms in multi-stand mills. On the other hand, complex MIMO models were widely adapted to simulate rolling chatter in the time domain by numerical methods and, as such, they were not suitable for stability analysis. In order to create a stability chart using simulations, the marginally stable cases have to be found. However, finding these marginal cases, using simulations, could be tedious and inaccurate. So it is desirable to formulate a MIMO chatter model, which is suitable for analytical model-based stability analysis.Although many studies have been conducted ...
Based on the general linear chatter model of a single-stand mill, derived in Part 1, two physical mechanisms that may lead to chatter will be explored. The first, termed instability caused by the 'model-matching effect', is the consequence of a simple process-structure interaction that exhibits a relatively high margin of stability. The second, 'mode coupling', is the consequence of multiple vibration modes. The stability of both chatter modes will be established by formulating analytical stability criteria in terms of relevant rolling process parameters. Simulation results will be presented to demonstrate stable and unstable mill behaviour.
We present a case of recurrent autoimmune hypoglycemia induced by non-hypoglycemic agents. We review reported cases of autoimmune hypoglycemia related to non-hypoglycemic agents, and discuss the effects of different detection methods for insulin autoantibodies on the results obtained. We aim to provide information for clinicians and a warning for medication usage. Considering the increasing number of clopidogrel-induced AIH cases and the hypoglycemia-induced increase in the risk of cardiovascular events, we recommend that cardiovascular disease patients being treated with clopidogrel be informed of this rare side effect and that clinicians be vigilant for the possibility of autoimmune hypoglycemia in this patient population.
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