A semi-analytical multi-harmonic balance method on full-3D contact model for dynamic analysis of dry friction systems

IF 5.3 1区工程技术 Q1 ENGINEERING, AEROSPACE

Chinese Journal of Aeronautics Pub Date : 2023-12-05 DOI:10.1016/j.cja.2023.11.026

He SUN , Dayi ZHANG , Yaguang WU , Qingyang SHEN , Dianyin HU

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引用次数: 0

Abstract

Dry friction damping structures are widely-used in aero-engines to mitigate vibration. The nonlinear nature of friction and the two-dimensional in-plane motion on the contact interface bring challenges to accurately and efficiently predict the forced response of frictionally damped structures. The state-of-the-art Multi-Harmonic Balance Method (MHBM) on quasi-3D contact model in engineering cannot precisely capture the kinematics on the friction interface although the efficiency is high. The full-3D contact model can describe the constitutive relationship of the interface in a more accurate manner; however, the efficiency and convergence are not guaranteed for large-scale models. In this paper, a semi-analytical MHBM on full-3D contact model is proposed. The original Trajectory Tracking Method (TTM) for evaluating the contact force is reformulated to make the calculation more concise and the derivation of the Analytical Jacobian Matrix (AJM) feasible. Based on the chain rule of derivation, the AJM which is the core to upgrade the performance is deduced. Through a shrouded blade finite element model, the accuracy and efficiency of the proposed method are compared with both the MHBM on full-3D contact model with numerical Jacobian matrix and the MHBM on quasi-3D contact model with AJM. The results show that the AJM improves significantly the efficiency of the MHBM on full-3D contact model. The time cost of the proposed method is in the same order of magnitude as that of the MHBM on quasi-3D contact model. We also confirm that the full-3D contact model is necessary for the dynamic analyses of shrouded blades. If one uses the quasi-3D model, the estimation relative error of damping can even reach 31.8% in some cases. In addition, the AJM also brings benefits for stability analysis. It is highly recommended that engineers use the MHBM on full-3D contact model for the dynamic analysis and design of shrouded blades.

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用于干摩擦系统动态分析的全三维接触模型半分析多谐平衡法

干摩擦阻尼结构被广泛应用于航空发动机，以减轻振动。摩擦的非线性性质和接触界面上的二维平面内运动为准确有效地预测摩擦阻尼结构的受迫响应带来了挑战。工程学中最先进的准三维接触模型多谐波平衡法（MHBM）虽然效率高，但无法精确捕捉摩擦界面上的运动学特性。全三维接触模型可以更精确地描述界面的构成关系，但对于大规模模型，其效率和收敛性无法保证。本文提出了一种基于全三维接触模型的半解析 MHBM。对原有的接触力轨迹跟踪法（TTM）进行了重新表述，使计算更加简洁，分析雅各布矩阵（AJM）的推导更加可行。根据推导的链式规则，推导出了作为提升性能核心的 AJM。通过一个带罩叶片有限元模型，比较了所提方法与使用数值雅各布矩阵的全三维接触模型 MHBM 和使用 AJM 的准三维接触模型 MHBM 的精度和效率。结果表明，AJM 显著提高了全三维接触模型上 MHBM 的效率。所提方法的时间成本与准三维接触模型上的 MHBM 在数量级上相同。我们还证实，全三维接触模型对于护罩叶片的动态分析是必要的。如果使用准三维模型，阻尼的估计相对误差在某些情况下甚至会达到 31.8%。此外，AJM 还能为稳定性分析带来好处。强烈建议工程师在全三维接触模型上使用 MHBM 对叶片进行动态分析和设计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Chinese Journal of Aeronautics 工程技术-工程：宇航

CiteScore

10.00

自引率

17.50%

发文量

3080

审稿时长

55 days

期刊介绍： Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice, such as theoretical research articles, experiment ones, research notes, comprehensive reviews, technological briefs and other reports on the latest developments and everything related to the fields of aeronautics and astronautics, as well as those ground equipment concerned.