基于双重响应面法的航空发动机叶片振动概率分析

Vibration Probability Analysis of Aero-Engine Blades Based on Double Response Surface Method

为了更精确地研究航空发动机叶片通过共振转速区发生短时间共振时的可靠性,在考虑共因失效(由振动一种因素引起的叶片变形和应力失效)的基础上,提出了航空发动机振动可靠性分析方法的双重响应面法。通过模态分析和谐响应分析得到叶片的最大变形和最大应力,选取密度、转速和气动力为输入变量,变形和应力为输出响应,建立了叶片最大变形和最大应力的响应面数学模型,在考虑转速、气动力、材料密度的基础上,得出了叶片的可靠性。分析结果表明:当叶片的允许变形量均值为2.45mm,方差为0.0368 mm,许用应力均值为540MPa,方差为8.1 MPa时,可靠性概率为99.14%。通过与Monte-Carlo法进行比较,验证了双重响应面方法在叶片发生短时间共振中的可行性和有效性。

In order to study the more accurate reliability of aero-engine blades when through out the region of resonance speed and occurred a short time resonance, considering the failure caused by common cause （the failure of stress and deformation caused by one factor of blade vibration）, the double response surface method was proposed. The blade maximum deformation and stress were obtained through the modal analysis and harmon- ic response analysis. Selected the density, speed and aerodynamic force as input variables and deformation and stress as output response, the response surface mathematical model of the blade maximum deformation and stress was established. The blade reliability was obtained based on considering the speed, the aerodynamic force and material density. The results show that the reliability is 99.14% when the mean of blade allowable deforma- tion is 2.45mm and variance of blade allowable deformation is 0.0368mm, the mean of blade allowable stress is 540MPa and variance of blade allowable stress is 8.1 MPa. Compared with the Monte-Carlo method , the feasi- bility and effectiveness of the double response surface method are validated when the blade occurs a short time resonance.