考虑偏峰统计特征的压气机叶栅前缘半径加工误差不确定性量化

doi:10.7527/S1000-6893.2024.30366

Abstract

Abstract:

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.

Key words: machining error, skewness, kurtosis, statistical distribution, uncertainty analysis

CLC Number:

V231.3

Yue DAN, Limin GAO, Huawei YU, Ruiyu LI, Qiusheng LUO, Yuyang HAO. Uncertainty quantification of leading-edge radius machining error of compressor cascade considering statistical characteristics of skewness and kurtosis[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(19): 630366.

Figures/Tables 22

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References 26

1	陈懋章，刘宝杰. 风扇/压气机气动设计技术发展趋势——用于大型客机的大涵道比涡扇发动机［J］. 航空动力学报， 2008， 23（6）： 961-975.
	CHEN M Z， LIU B J. Fan/compressor aero design trend and challenge on the development of high bypass ratio turbofan［J］. Journal of Aerospace Power， 2008， 23（6）： 961-975 （in Chinese）.
2	MANSOUR G. A developed algorithm for simulation of blades to reduce the measurement points and time on coordinate measuring machine （CMM）［J］. Measurement， 2014， 54： 51-57.
3	BOLOTOV M A， PECHENIN V A， RUZANOV N V. Uncertainties in measuring the compressor-blade profile in a gas-turbine engine［J］. Russian Engineering Research， 2016， 36（12）： 1058-1065.
4	LIU C Q， LI Y G， SHEN W M. A real time machining error compensation method based on dynamic features for cutting force induced elastic deformation in flank milling［J］. Machining Science and Technology， 2018， 22（5）： 766-786.
5	HOU Y H， ZHANG D H， MEI J W， et al. Geometric modelling of thin-walled blade based on compensation method of machining error and design intent［J］. Journal of Manufacturing Processes， 2019， 44： 327-336.
6	GARZON V E， DARMOFAL D L. Impact of geometric variability on axial compressor performance［J］. Journal of Turbomachinery， 2003， 125（4）： 692-703.
7	MANOHARA SELVAN K， KOWALCZYK L. Exploring the impact of manufacturing geometric uncertainties on the aerodynamic performance of a small scale compressor［R］. New York： ASME， 2018.
8	罗佳奇，陈泽帅，曾先. 考虑几何设计参数不确定性影响的涡轮叶栅稳健性气动设计优化［J］. 航空学报， 2020， 41（10）： 123826.
	LUO J Q， CHEN Z S， ZENG X. Robust aerodynamic design optimization of turbine cascades considering uncertainty of geometric design parameters［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（10）： 123826 （in Chinese）.
9	李玉，楚武利，姬田园. 叶片安装角偏差对动叶性能影响的不确定性研究［J］. 西安交通大学学报， 2023， 57（4）： 49-59.
	LI Y， CHU W L， JI T Y. Uncertainty research of effects of blade stagger angle deviation on the performance of rotor［J］. Journal of Xi’an Jiaotong University， 2023， 57（4）： 49-59 （in Chinese）.
10	蔡宇桐，高丽敏，马驰，等. 基于NIPC的压气机叶片加工误差不确定性分析［J］. 工程热物理学报， 2017， 38（3）： 490-497.
	CAI Y T， GAO L M， MA C， et al. Uncertainty quantification on compressor blade considering manufacturing error based on NIPC method［J］. Journal of Engineering Thermophysics， 2017， 38（3）： 490-497 （in Chinese）.
11	刘佳鑫，于贤君，孟德君，等. 高压压气机出口级叶型加工偏差特征及其影响［J］. 航空学报， 2021， 42（2）： 342-358.
	LIU J X， YU X J， MENG D J， et al. State and effect of manufacture deviations of compressor blade in high-pressure compressor outlet stage［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（2）： 342-358 （in Chinese）.
12	罗佳奇，陈泽帅，邹正平，等. 低压涡轮铸造叶片几何不确定性统计［J］. 航空学报， 2023， 44（6）： 305-320.
	LUO J Q， CHEN Z S， ZOU Z P， et al. Statistics on geometric uncertainties of casting blades in low-pressure turbines［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（6）： 305-320 （in Chinese）.
13	WANG X J， DU P C， YAO L C， et al. Uncertainty analysis of measured geometric variations in turbine blades and impact on aerodynamic performance［J］. Chinese Journal of Aeronautics， 2023， 36（6）： 140-160.
14	李志国，彭宇轩，秦川，等. 大跨曲面屋盖脉动风荷载非高斯分布特性试验研究［J］. 工业建筑， 2021， 51（7）： 84-89.
	LI Z G， PENG Y X， QIN C， et al. Experimental study on non-gaussian distribution characteristics on fluctuating wind loads on a long-span curved roof［J］. Industrial Construction， 2021， 51（7）： 84-89 （in Chinese）.
15	SANDERS J L， EVANS N W. Near-Gaussian distributions for modelling discrete stellar velocity data with heteroskedastic uncertainties［J］. Monthly Notices of the Royal Astronomical Society， 2020， 499（4）： 5806-5825.
16	TIAN Z X， LI B. Threshold speed of short journal bearings considering the non-Gaussian longitudinal surface roughness［J］. Proceedings of the Institution of Mechanical Engineers， Part J： Journal of Engineering Tribology， 2022， 236（11）： 2138-2145.
17	JONDEAU E， ROCKINGER M. Gram-Charlier densities［J］. Journal of Economic Dynamics and Control， 2001， 25（10）： 1457-1483.
18	TAMANDI M， JAMALIZADEH A. Finite mixture modeling using shape mixtures of the skew scale mixtures of normal distributions［J］. Communications in Statistics-Simulation and Computation， 2020， 49（12）： 3345-3366.
19	LIU C H， RUBIN D B. The ECME algorithm： A simple extension of EM and ECM with faster monotone convergence［J］. Biometrika， 1994， 81（4）： 633-648.
20	MA C， GAO L M， WANG H H， et al. Influence of leading edge with real manufacturing error on aerodynamic performance of high subsonic compressor cascades［J］. Chinese Journal of Aeronautics， 2021， 34（6）： 220-232.
21	高丽敏，王浩浩，杨光，等. 关于叶片前缘加工缺陷及气动合格性的探讨［J］. 推进技术， 2023， 44（1）： 76-85.
	GAO L M， WANG H H， YANG G， et al. Discussion on machining defects of blade leading edge and aerodynamic qualification［J］. Journal of Propulsion Technology， 2023， 44（1）： 76-85 （in Chinese）.
22	庄皓琬，滕金芳，朱铭敏，等. 考虑加工公差的叶片对压气机气动性能的影响［J］. 上海交通大学学报， 2020， 54（9）： 935-942.
	ZHUANG H W， TENG J F， ZHU M M， et al. Impacts of blades considering manufacturing tolerances on aerodynamic performance of compressor［J］. Journal of Shanghai Jiao Tong University， 2020， 54（9）： 935-942 （in Chinese）.
23	师义民，徐伟，秦超英，等. 数理统计［M］. 北京：科学出版社， 2015.
	SHI Y M， XU W， QIN C Y， et al. Mathematical statistics［M］. Beijing： Science Press， 2015 （in Chinese）.
24	马驰. 不确定性量化方法研究及压气机多源不确定性气动性能预测［D］. 西安：西北工业大学， 2022.
	MA C. Research on uncertainty quantification method and prediction of the aerodynamic performance of compressors caused by multisource uncertainties［D］. Xi’an： Northwestern Polytechnical University， 2022 （in Chinese）.
25	WITTEVEEN J A S， BIJL H. Modeling arbitrary uncertainties using gram-schmidt polynomial chaos： AIAA-2006-0896［R］. Reston： AIAA， 2006.
26	WANG H H， GAO L M， YANG G， et al. A data-driven robust design optimization method and its application in compressor blade［J］. Physics of Fluids， 2023， 35（6）： 066114.

参数	数值
均值μ/mm	0.022
标准差σ/mm	0.023
偏度Sk	-0.849
峰度Ku	4.581

参数	最大似然估计
位置参数ξ	0.012
尺度参数σ	0.024
形状参数λ	1.194
形状参数α	2.009
随机数ν₁	0.247
随机数ν₂	0.634

统计分布	lnL
Normal	234.611
SMSCN	236.837

统计分布	D_n
Normal	0.073
SMSCN	0.043

N	正交基函数
0	1
1	x-0.022 5
2	x²-0.040 2x-0.000 2
3	x³-0.056 8x²-0.000 9x
4	x⁴-0.073 5x³-0.021 8x²+0.000 1x

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

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几何参数	数值
弦长c/mm	69.95
栅距t/mm	30.43
安装角θ/（^o）	26.58
进口角β_1k/（^o）	45.83
前缘半径R₀/mm	0.52

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统计分布	Rat
Normal	0.451
SMSCN	0.734

统计分布	Rat
Normal	0.560
SMSCN	0.272