中文摘要：

基于2006年研究生数学建模C题《维修线性流量阀时的内筒设计问题》,主解决了两个问题,问题一：能否通过选择内筒孔形状实现“过流面积”与内筒旋转角度成严格的线性关系;问题二：在实际工作中,由于固井机的主工作区存在一定的范围制约,所以在这种制约条件下,我们如何设计内筒孔形状,才能使固井机的主工作区尽量大？在文中主采用变分法来解决这两个问题。

英文摘要：

This research is based on the Maintenance Tube Design Problems, mainly to 2006 graduate C mathematical modeling topic Linear Flow Valve solve two problems, problem one： whether the ＂flow area＂ and inner cylinder rotation angle into a strict linear relationship could be realized by selecting the inner cylinder hole shape; problem two： in the practical work, there is a certain range restriction in the main work area of the ce- menting machine, so in this condition, how to design the inner hole shape to make the main work area cementing machine as large as possible？ In this paper, the variational method is used to solve these two problems.