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给出了扩展多阶多项式拟合公式及等效阶次和评定误差的算法,并利用Matlab编制了相应的拟合函数和计算函数。以此为工具,针对同一典型真实标定曲线,研究了5组28种拟合公式的拟合情况。研究表明,选用合适的正负阶次多项式拟合,可在减少计算复杂度的同时,降低拟合误差,增强拟合效果。在叶尖间隙标定精度小于0.01 mm、电压采集误差小于2.5 mV的情况下,±3阶多项式拟合为该系统标定曲线的最佳拟合方式。
The algorithm of extending multi-order polynomial fitting formula and equivalent order and evaluating error is given. The corresponding fitting function and calculating function are compiled by Matlab. Using this as a tool, the fit of 28 fitting formulas of 5 groups was studied for the same typical real calibration curve. The research shows that choosing suitable positive and negative order polynomial fitting can reduce the computational complexity, reduce the fitting error and enhance the fitting effect. With tip clearance calibration accuracy less than 0.01 mm and voltage acquisition error less than 2.5 mV, the ± 3 order polynomial fitting is the best fit for the calibration curve of the system.