直-增-稳剖面设计问题的解析解

Analytical Solutions of Straight-Buildup-Stable Profile Design

摘要:

使用无量纲化方法对设计方程组进行了改写，新的无量纲化设计方程组有利于充分利用三角函数公式求解析解，所得到的解析解计算公式具有简洁的数学形式。将设计方程组求解问题分成两类，对于已知最大井斜角的第Ⅰ类问题，使用线性代数解方程组的克莱默法则直接就可以得出解析解。最大井斜角为未知数的第Ⅱ类问题，使用三角函数公式进行化简，得到形式简单、统一的解析解公式，避免了使用半角公式所带来的解析解计算公式的复杂性。所使用无量纲化方法具有一定的普适性，可以用于解决其他类型的二维剖面设计问题。

Abstract:

Dimensionless method is used to rewrite designing equations. The new dimensionless designing equations is of advantage to solving analytical solutions by using trigonometric function formula. The analytical solutions has simple mathematical form. The resolution of the designing equations is classified into two categories. For Class I problems with known maximum deviation angle, the analytical solutions can be derived directly by using the Cramer law of linear equations. For Class II problems with unknown maximum deviation angle, trigonometric function formulas is used to derive simple and uniform formula of analytical solutions, and to avoid the complexity of semi-angle equation for solving analytical solutions. Dimensionless method has certain universality and can be used to solve other 2D profile designing problems.