Abstract: Aiming at the difficulties in identifying modal damping of high-speed rotating blades，a novel method named phase tangent slope method was proposed. In the method，the tip timing technique was used to obtain vibration response of blades，and the tangent slope of phase-frequency curve at resonant point was employed to calculate modal damping ratio. After the Lagrange interpolation of the preliminary phase-frequency data，the tangent slope at resonant point was obtained through central difference. Tip timing theory was introduced，and then theory of phase tangent slope method was also presented，and it was applied in the damping identification of simulated damping and actual high-speed rotating centrifugal blades. The results demonstrated that error of the phase tangent slope method can reach up to 1×10-4 % and is significantly smaller than the maximum error 53.68 % of the half-power bandwidth method as long as the interval of frequency ratio is small enough (e.g. 1×10-6). In the modal damping identification of rotating blades，the identified results of the phase tangent slope method，the half-power bandwidth method and Hood software can be comparable in magnitude. Modal damping ratios of various blades show a certain degree of dispersion，while all the values fall within the scope of 8.0×10-4 to 1.2×10-3. It indicates that the identification results of the phase tangent slope method are reliable and credible.

Key words: High-speed rotating blade；Blade tip timing；Damping determination；Vibration response

摘要： 针对高速旋转叶片阻尼识别难的问题，提出了一种利用叶尖定时技术获取叶片振动响应，进而由相频曲线在共振点的切线斜率求取模态阻尼比的新方法——相位切线斜率法。对原始相频数据进行拉格朗日插值后，再由中心差分得到共振点处的切线斜率。介绍了叶尖定时理论，阐述了相位切线斜率法原理，并将其应用于仿真阻尼与实际高速旋转离心叶片阻尼的识别当中。结果表明，相位切线斜率法在满足频率比间隔足够小(例如1×10-6)时，误差可达到1×10-4 %数量级，远小于半功率带宽法的最大误差53.68 %。在旋转叶片模态阻尼识别中，相位切线斜率法、半功率带宽法和Hood软件识别结果存在数量级上的可比性；不同叶片的模态阻尼比呈现一定的分散性，但总体落在8.0×10-4～1.2×10-3的范围内。由此说明，相位切线斜率法识别结果可靠可信。

关键词: 高速旋转叶片；叶尖定时；阻尼测定；振动响应