基于新息优化模型GM(1,1,α)的螺旋锥齿轮磨削加工表面粗糙度预测

Surface Roughness Forecasting of Spiral Bevel and Hypoid Gear Based on Newest Information Optimized Gray Model GM(1,1,α)

影响螺旋锥齿轮磨削加工表面粗糙度Ra值的因素众多且很多不明确,该Ra值的预测属典型的灰色问题。本文根据新息优先原理,通过改变GM(1,1,D)的边界条件和白化背景值z(1)(k)的选取方式,得到新息优化GM(1,1,α)模型。实验证明,用新息优化GM(1,1,α)模型预测螺旋锥齿轮的磨削加工表粗糙度可获得平均相对误差小于1%的高精度预测结果。

Because the value of Ra is affected by a lot of facts and some of them are undefined, the surface roughness forecasting of spiral bevel and hypoid gears is a typical gray system. It is discussed in the paper that based on the priority principle of the newest information, the newest information optimized gray model GM（ 1,1, a ） can be got by changing the choice of the initial condition and the white background series z^（1） （ k ） in gray model GM（ 1,1, α）. The experiment data proves that the model GM（ 1, 1, α）could not only be used in forecasting the surface roughness of spiral bevel and hypoid gears, but also get a more precise result that the average relative error is less than 1%.