Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.
