A new calculation method of critical wind speed based on three degrees of freedom (3-DOF) is proposed for galloping problem of iced transmission line. Based on the quasistatic theory, the aerodynamic load of iced transmission line is obtained, which considers the influence of transverse and torsional motion on the relative wind angle of attack. Finally, the equivalent galloping model of 3-DOF iced transmission line is established. At the initial angle of attack, the aerodynamic load is expanded by Taylor, and the unsymmetrical linear aerodynamic coefficient matrix is obtained. The Routh–Hurwitz criterion is used to judge the stability of iced transmission line system, and then the critical wind speed is calculated. The in-plane and out-plane frequencies corresponding to the first-order mode of the transmission line are solved by the analytical method and numerical simulation method. The results obtained by the two methods are compared and verified. The influence of dimensionless transmission line parameter λ on the in-plane and out-of-plane frequencies is discussed. The aerodynamic coefficients of the iced transmission line are measured by wind tunnel test and the aerodynamic characteristics are analyzed. According to the theoretical formula, the critical wind speed is calculated by MATLAB. The critical wind speed determined in this paper is compared with the critical wind speed determined by Den Hartog and Nigol theory. The influences of torsional vibration frequency, ice thickness, and ice shape on critical wind speed are analyzed. The research results of this paper have important theoretical significance for the stability judgment of iced transmission lines.

中文翻译：

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基于三自由度的冰输电线路的舞动稳定性和空气动力特性

提出了一种基于三自由度（3-DOF）的临界风速计算方法，以解决输电线路的疾驰问题。基于准静态理论，考虑了横向和扭转运动对相对风迎角的影响，得出了冰输电线路的气动载荷。最后，建立了三自由度冰输电线路的等效驰豫模型。在初始迎角下，泰勒扩展了空气动力载荷，并获得了非对称线性空气动力系数矩阵。Routh–Hurwitz准则用于判断结冰的输电线路系统的稳定性，然后计算临界风速。通过解析法和数值模拟法求解与传输线的一阶模式相对应的面内和面外频率。比较和验证了通过两种方法获得的结果。无量纲输电线路参数的影响讨论了平面内和平面外频率上的λ。通过风洞试验测量了结冰的输电线路的空气动力系数，并对空气动力特性进行了分析。根据理论公式，利用MATLAB计算出临界风速。将本文确定的临界风速与由Den Hartog和Nigol理论确定的临界风速进行比较。分析了扭转振动频率，冰厚和冰形对临界风速的影响。本文的研究结果对于冰输电线路的稳定性判断具有重要的理论意义。