| During the cold rolling of plate, longitudinal direction residual stress exists in the rolled plate for the ill-distributed metal deformation. When residual stress overrides limit, plate will create destabilizing buckling deformation and billows. The task of shape discrimination mode is to discriminate whether shape is destabilizing by the measured residual stress distribution of shape instrument, which determinates whether the control system adjusts shape. This paper fits cross-direction bending function of plate with three-spline function. This function not only makes bending bit shift and corner meet geometry edge condition but also makes plate bending moment satisfy force edge condition. This method can choose the same bending function to different type of residual stress, can greatly reduce the number of strip elements and improve the calculation speed also. Based on small-deflection theory, this paper brings forward critical parameter that enhances or reduces residual stress, which makes plate in critical state. This paper converses stability discriminating problem into characteristic value problem by least power theory, solves discrimination parameter and corresponding critical bending half wavelength combined with one-dimension hunting. According to the type of residual stress distribution, it analyses the longitudinal direction restraint of plate edge or middle, discusses the influence of plate width-thick ratio and residual stress deviation to discrimination parameter and bending half wavelength. This paper establishes whole stability discrimination mode, works out programs of shape discrimination mode, and formats a set of shape discriminating and analyzing software that based on spline method. Large quantity of experiment data has been calculated by the software, and the results approve that the software computes accuracy and fast. It brings forward theory foundation and method for establishing the mathematical mode of shape control. |
