It is very important to create a useful cyclic symmetric model for the investigation of the vibration reduction effect of hard-coating blisk. This study aims to develop a cyclic symmetry algorithm which can determine the mode of blisk in the sector coordinate system directly.,Using the exponential and real quasi-equivalent Fourier matrices, the formulas for solving the sector mode were derived, and the relationship between the two kinds of sector modes was also discussed. Based on the proposed cyclic symmetry algorithm, the vibration characteristics of an academic blisk were solved, and the formulas for solving the natural characteristics and vibration responses of the coated blisk were given.,A blisk with NiCrAlCoY+YSZ hard coating on both sides of each blade was chosen as a case to demonstrate the presented method. Based on the verification analysis model, the influences of coating thickness on the vibration reduction effect of the blisk were discussed. The results show that the hard coating has good vibration reduction effect on the blisk even the coating thickness is very thin and the vibration reduction effect of hard coating in the high frequency range is obviously better than that in the low frequency range.,As a large number of reduced order modeling methods of blisk are implemented based on the sector modes, the proposed method which can obtain the sector modes directly will significantly improve the efficiency of dynamic modeling and analysis of the coated blisk structure.

中文翻译：

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用于研究硬涂层叶盘减振的循环对称模型

创建一个有用的循环对称模型对于研究硬涂层叶盘的减振效果非常重要。本研究旨在开发一种循环对称算法，该算法可以直接确定扇形坐标系中叶盘的模态。,利用指数和实数拟等价傅立叶矩阵，推导出扇形模态的求解公式，并分析了叶盘模态与叶盘模态之间的关系。还讨论了两种扇区模式。基于所提出的循环对称算法,求解了某学术叶盘的振动特性,并给出了涂层叶盘的固有特性和振动响应的求解公式。,双面有NiCrAlCoY+YSZ硬涂层的叶盘选择刀片作为案例来演示所提出的方法。基于验证分析模型，讨论了涂层厚度对整体叶盘减振效果的影响。结果表明,即使涂层厚度很薄,硬涂层对叶盘的减振效果也很好,而且硬涂层在高频范围内的减振效果明显优于低频范围。,作为一个大基于扇形模态实现了多种叶盘降阶建模方法，所提出的可直接获取扇形模态的方法将显着提高涂层叶盘结构动态建模和分析的效率。