含接触界面的叶片非线性模态分析方法

Nonlinear Modal Analysis Method for Blades with Contact Interfaces

关键词:  接触界面  叶片  阻尼非线性模态  多谐波平衡法  能量平衡

Key words:  Contact interfaces  Blades  Damped nonlinear normal modes  Multi-harmonic balance method  Energy balance

摘要:

为揭示含复杂接触界面的大规模叶片的非线性模态特性，建立了含接触界面的叶片非线性模态高效分析方法。以含缘板阻尼器的简化涡轮叶片有限元模型为例，介绍了含接触非线性耗散系统的阻尼非线性模态的基本定义；综合采用多谐波平衡法和基于高精度频响函数矩阵的线性自由度压缩方法，将非线性计算规模降低至初始模型的1/88，实现了含接触界面的大规模叶片有限元模型的非线性模态高效分析；基于能量平衡思想探索了叶片阻尼非线性模态振动与其共振点强迫振动响应之间的关联。结果表明，该非线性模态分析方法能够同步揭示叶片非线性模态频率和非线性阻尼比的振幅相关特性，对于涡轮叶片的动力学设计和缘板阻尼器的减振能力的量化评估具有重要意义。

Abstract:

In order to carry out nonlinear modal analysis for large-scale blade models with complex contact interfaces， a computationally efficient nonlinear modal analysis method for blades with contact interfaces is established. This method is exemplified in a finite element model of simplified turbine blades with an under-platform damper. Firstly， the concept of damped nonlinear normal modes is introduced for the nonlinear system with dissipative contact nonlinearity. Secondly， by employing the multi-harmonic balance method and the linear degree-of-freedom condensation technique in conjunction with an accurate frequency response function matrix approximation， the nonlinear computational cost is reduced to 1/88 that of the original model. It allows to perform the nonlinear modal analysis with high computational efficiency for the large-scale finite element model of blades with contact interfaces. Finally， the correlation between the damped nonlinear normal modes （dNNM） and the forced vibration response at nonlinear resonance is explored by means of the energy balancing concept. Numerical case studies demonstrate that the established nonlinear modal analysis method allows to predict the amplitude-dependent nonlinear modal frequency and nonlinear modal damping ratio. This is of significant importance for the safe design of the turbine blade dynamics， as well as the quantitative evaluation of the capability of the friction damper.