建立了由样条函数表示的螺旋锥齿轮副齿面接触点的求解模型———带区间的五元三次非线性方程组 .为了避免拟牛顿法解带区间非线性方程组不收敛的缺陷 ,将此方程组转化为一带约束优化求极小值问题 ,并选用复合形法使问题得以解决 .所提出的方法具有简单、稳定、可靠、不要求选取初始点及计算过程中只需用到目标函数值等优点 The solving model of the contact point of spiral bevel gear’s flank surface, which is represented by the spline function, is established. In this paper, the quintic cubic nonlinear equations with interval are established. In order to avoid the defect that non-linear equations in solution interval of quasi-Newton method converge, This equation is transformed into a minimization problem with constrained optimization, and the complex method is adopted to solve the problem.The proposed method is simple, stable and reliable, does not require to select the initial point and only need to use the target Function value and so on