Uncertainty quantification of leading-edge radius machining error of compressor cascade considering statistical characteristics of skewness and kurtosis

The issue of geometric uncertainty of compressor blade machining is very prominent. As the input of the uncertainty quantification system, the accurate expression of its statistical distribution is particularly important for the system output. According to the statistical analysis of leading-edge radius errors at the same blade height section of 100 compressor rotor blades, it is found that the distribution is left-skewed and in a peak condition, with significant non-normality. Then, to overcome the limitations of the normal distribution, the expectation conditional maximization either method is used to obtain the error distribution with skewness and kurtosis, which fits the error data better than the normal distribution. Finally, the leading-edge radius error fitting the two distributions are used as the uncertainty quantification input separately, and the total pressure loss coefficient and static pressure ratio of the cascade are used as the response. Comparison of the quantification results shows that the total pressure loss coefficient and static pressure ratio mean variable values, the mean variable values of the total pressure loss coefficient and static pressure ratio corresponding to different statistical distribution are less than 1%, which can be negligible, while the scatter difference is significant. Besides, the variation of the total pressure loss coefficient is larger than that of the static pressure ratio, about 20% at most. In addition, if the normal distribution is input, the influence of the uncertainty of the leading-edge radius error on the scatter of the cascade aerodynamic performance and the performance variation range are significantly overestimated, while the possibility of performance deterioration is underestimated. This research illustrates the necessity of considering skewness and kurtosis characteristics of machining errors to provide more accurate reference for blade fine machining.