Theoretical Analysis For Plate Leveling Process And Its Control System

The plate leveling process is an elastic-plastic bending deformation process during which loading and unloading take place alternatively. In addition, the contact relationship between the plate and roll series is nonlinear. So the precise analysis of leveling process is very diffcult. At present, many problems of leveling process need to be analyzed systematically and theoretically. However, the traditional theoretical analysis has low precision and much limitation, because it is always based on the bending beam theory. So it is very necessary to build the new method of the systematic and precise theoretical analysis of leveling process. Therefore, the theoretical derivation and systematical analysis were performed with methods of curvature integration, finite difference and residual stress increment. Furthermore, the studies on mathematical models, curvature analysis, residual stress, buckling and process optimization during roller leveling process were carried out. According to the device and technology conditions of a certain factory, a plate leveling process control system was developed. The specific contents are shown as follows:(1) Mathematical models for plate leveling process control were established. For the first time in China, the stress analysis of plate leveling process was done by using the Prandtl-Reuss plastic incremental law. Based on the experimental data, the relationships between temperature and Young’s modulus or yield stress were given according to different steel grades in the whole range of temperature. The leveling speed formula was put forward. The defined biting ratio was regarded as biting criterion. The One-Dimensional implicit temperature model was used to calculate the temperature drop of leveling process. The experimental formula was adopted as the initial intermesh setting one. In addition, the spring formula of leveler was given.(2) The Two-Dimensional analytic method of curvature for plate leveling process was built. For the first time, the geometric equations of contact between the plate and rollers were deduced according to two different kinds of bending leveling fields in which the first roller was up or down. Then, the recursion formulas of curvature and slope angle and the formula of initial slope angle were deduced with the curvature integral method. Based on the equilibrium equation of stress, the integral formula of curvature variable was also derived. Using the finite increment method, the integral values of curvature variables were calculated. So the Two-Dimensional iterative new method of curvature analysis was given. The predicted values of this method were in accord with experimental ones. Therefore, the precision of the method is very high. Since the cumulative effect of curvature exists, it is necessary to adopt the rational skew value to remove the side effect of cumulative effect. To obtain better leveling effect, it is necessary to set the higher plastic deformation ratio about 80% and use the appropriate exit intermesh that minimizes the residual curvature.(3) The Three-Dimensional analytic method of residual stress for plate leveling process was built. The Three-Dimensional geometrical element division of plate was made. Based on the stress equilibrium equation and the deformation compatibility equation, the linear strain increment equations of central thickness line were deduced. The stress increment calculation method was given for each element along width of Three-Dimensional geometric solid. The formula of residual stress after leveling was also derived. So the iterative new method of residual stress calculation was given. In addition, the two types of evaluation criterion for residual stress along thickness or width were put forward. The predicted values of this method were in accord with experimental ones. So the validity of the method was proved. At the same time, studies on the relationships between plastic deformation, bending value, tension stress and residual stress were carried out respectively. After some calculations and analysis, the optimum leveling condition under the condition of single initial curvature was given.(4) Studies on buckling of plate after leveling were carried out. The calculation method of thermal stress during air cooling after leveling was put forward. Then, whether the buckling of plate on room temperature could take place was confirmed. In addition, the relationships between plastic deformation ratio, bending value and leveling ratio were studied respectively. After analysis, the thermal stress is the key reason why the shape defects of plate appear after leveling. Finally, the countermeasures for different problems of residual stress after leveling were given.(5) Studies on leveling process optimization were carried out. Based on numerical calculation, the simplified formulas of maximum curvature, plastic deformation ratio, residual curvature, residual stress and residual steepness were put forward. The multiple target optimization function of intermesh allocation was also given. Based on control strategy of model, the variable metric algorithm of BFGS was adopted to calculate the optimum leveling process. This method of leveling process optimization was proved feasible by comparison of practical values.(6) The leveling process control system was developed. Under the special conditions of devices and process, the leveling process control system platform was designed, including the functions of communication, plate tracking, monitor, set, maintenance and so on. The online adjustment parameter table was built through offline calculation. The online leveling process schedule was gotten by chiefly querying the adjustment parameter table or besides by online leveling process optimization calculation. Moreover, the grade table of leveling process was set up. Furthermore, the function of self-learning was advanced.Thus, the much better leveling theory of plate has been set up. The formulas of curvature and residual stress are deduced. Later, the leveling process model simulation system of plate and the leveling process online control system have been developed successfully. The simulation system has been checked and accepted. The online control system has been debugged and applied. It can implement the preset function of leveling process.