二维S型剖面设计问题的解析解

Analytical solution of two-dimensional profile problem

二维S型剖面设计问题可以归结为求解一个二元方程组,根据已知设计参数的情况,可以分成21种不同的未知数组合情况进行求解。使用无量纲化思想改写原设计方程组,并根据角度未知数在方程组中出现的位置,将方程组求解问题归并成四类问题,每类问题求解方法具有相似性。推导出了21种不同情况下的解析解计算公式,所得到的计算公式具有比较简洁的数学形式。求解析解过程中所使用的无量纲化结合三角函数化简的方法为二维剖面设计问题求解提供了一种新的数学模式,适用于其他类型的二维圆弧型剖面设计问题解析求解。绘制设计参数取值范围图形是解析解的一个重要应用,可以使设计人员合理设定已知设计参数,减少试算次数,提高设计效率。所给出的解析解计算公式对于开发钻井设计软件也具有一定的指导意义。

Two-dimensional Stype profile design can be summed up in solving a binary equations.According to known design parameters of the situation,it can be divided into 21 different unknown numbers combinations.Use dimensionless thought,rewrite the original design.And according to the Angle unknowns equations appeared in equations of position,the equations solving problem merge into four types of problems,every kinds of problem solving method has similarities,which deduced analytical solution under21 different circumstances,the obtained formulas have more concise mathematical form.The dimensionless method combined with trigonometric simplifing in the analytical solution provided a new mathematical model to 2-D profiles designing and is applicable to other types of two-dimensional circular arc profile design problems.Drawing design parameter values range graphics is an important application of analytical solutions,it can make the designer to set unknown parameters reasonably,reduce calculating trial times,improve the design efficiency.The Given the analytical solution of the calculation formula also has certain directive significance for developing the drilling design software.