中文摘要：

在变厚度轧制典型产品TRB板和LP板节材效果日益引起人们重视的背景下，近年来变厚度轧制理论与技术得到了快速发展。本文提出了变厚度轧制过程中的力平衡微分方程（VGR—F方程）及质量守恒定律表述方式（VGR—S方程），为变厚度轧制的力学研究和运动学研究奠定了基础。国内外TRB板生产线的建成投产，推进了汽车轻量化进程，也为变厚度轧制研究提出了一系列新的课题。深入研究并解决这些问题，将推动变厚度轧制理论发展和技术进步，使该技术在节能减排中发挥出重要作用。

英文摘要：

Under the background of saving materials products such as TRB and LP attracting our more and more attention, recently the theory and application of Variable Gauge Rolling （VGR） is having a quick development. The recent research work on the differential equations of force equilibrium and the law of mass conservation for VGR leads to propose the VGR-F equation and the VGR-S equation, which provide a new base for further research on VGR. As the production line for TRB built up in domestic and abroad, a series new problena comes out, it will be not only playing an important role in the car lightweight, but also pushing a force for the roiling theory and application.