Dynamic Modeling And Stability Analysis Of Rolling Mill Coupling Vibration

Iron and steel industry is the basic industry of the national economy, and it has made great contributions for the rapid development of the national economy. Strips are the main products of the iron and steel industry. With the improvement of the industrial technology, the social requirement for the dimensional accuracy and the surface quality of strips has become increasingly strict. However, due to the existence of the rolling mill vibration, the improvement of the product quality and the production efficiency is seriously restricted. In this paper, the high speed strip rolling mill is taken as the research subject. The rolling mill multiple-modal-coupling modeling, the system stability analysis and the vibration control are systematic studied based on the theoretical analysis, the numerical simulation, the experimental verification and so on. The main research contents are as follows:(1) Taking a typical four high rolling mill as the research object, through the analysis of the vibration characteristics of different types of vibration, the simplifying method of the rolling mill coupling vibration structure model is explored by studying the rolling mill modal characteristics as well as the modal sensitivity to structure parameters. On this basis, a rolling mill coupling vibration structure model is established, in which the vertical vibration, torsional vibration and horizontal vibration can be well indicated. These studies can provide guidance for the simplification of the structure model of other rolling mills.(2) Based on the symmetry hypothesis as well as the uniform deformation assumption, and considering the work roll flattening effect and the strips strain hardening effect, a dynamic rolling process model, in which the rolling mill vertical vibration, torsional vibration and horizontal vibration are simultaneous incorporated, is formulated. In order to study the rolling vibration analytically, a linearization process is done to the dynamic rolling process model by using a first-order Taylor series approximation. These studies can lay the foundation for the establishment of the rolling mill vertical-torsional-horizontal coupled dynamic model as well as the analysis of the system stability.(3) The rolling mill vertical-torsional-horizontal coupled dynamic model is constructed by coupling the dynamic rolling process model and the rolling mill structure model. According to this mathematical model, the method of system stability analysis is explored. The system critical rolling speed is calculated, and the accuracy of the calculated results is verified by experimental data. Then the dynamic responses in both time and frequency domains are analyzed in the condition of the initial disturbance and the periodic disturbance respectively, and the instability mechanism of the system is revealed. Finally, the influences of the rolling process parameters and the rolling mill structure parameters on the system stability are analyzed. And a series of experiments is conducted to verify the correctness of these analysis conclusions. Among the controllable rolling process parameters, the influences of the reduction ratio, tensions at entry and exit and the friction coefficient are relatively larger. Among the structure parameters, the influences of the work roll radius, the distance L0, and the structure parameters of vertical subsystem are relatively larger. These results are helpful in formulating a reasonable technological procedure of the rolling process and determining a feasible dynamic modification strategy of the structure as well.(4) A classical nonlinear friction model is introduced to the dynamic rolling process model, and the rolling mill vertical-torsional-horizontal coupled dynamic model under nonlinear friction is established. On this basis, the system Hopf bifurcation points at different rolling speeds are calculated by Hurwitz algebraic criterion. And the system stability domain is determined by analyzing the eigenvalue of the system. The results show that the system stability domain is enclosed by the instability critical lines of vertical vibration modal, torsional vibration modal and horizontal vibration modal. Finally, the influences of the rolling process parameters and the rolling mill structure parameters on the system stability domain are analyzed and compared in detail. Among them, the main influencing parameters on vertical vibration modal are the distance L0, the reduction ratio, the structure parameters of vertical subsystem and the work roll radius. The main influencing parameter on torsional vibration modal is the reduction ratio. The main influencing parameters on horizontal vibration modal are the reduction ratio, the strip entry thickness, the distance L0 and the structure parameters of horizontal subsystem.(5) Based on the rolling mill coupled dynamic model under nonlinear friction, the Hopf bifurcation types at different bifurcation points are judged. The construction method of the controller is explored and put forward. Then, the controlling of the tension fluctuation at entry is taken as an example, and a linear and nonlinear state-feedback controller is constructed. On this basis, the linear control of the controller is studied using the Hurwitz algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. Finally, through the simulation analysis, the correctness and accuracy of the theoretical analytical results are checked, the effectiveness of the controller construction method as well as the designed controller is verified.