Wind action on ice-covered transmission lines causes galloping, which is a problem because it can introduce interphase short circuits and cause fatigue of the cross-arms of the power line’s towers and insulators. The galloping phenomenon is characterised by a combination of large-amplitude, low-frequency vertical, horizontal, and torsional oscillations. To better understand the dynamic responses of vertical, horizontal and torsional 3-degree-of-freedom (DoF) galloping on four-bundled conductors, time–history analyses were conducted for 2D systems of varying DoFs and frequency ratios. The fundamental characteristics of the conductor’s non-linear 1-DoF vertical response were analysed via time–history analysis, indicating that large oscillations were caused by inclusion of an angular range of relative angle of attack with a high negative lift-coefficient slope. By considering the energy balance of the vertical motion over one oscillation period, we estimated the stable and unstable limit-cycle amplitudes. Then, by comparing the results of the 1-, 2-, and 3-DoF systems, we clarified the effect of aerodynamic coupling on 3-DoF galloping. The oscillation types in the 3-DoF systems were categorised as vertical–horizontal 2-DoF coupling oscillations, vertical–torsional 2-DoF coupling oscillations, and vertical 1-DoF oscillations according to the stationary torsional angle. Finally, we indicated the coupling effects on vertical oscillation by considering the energy balance of the vertical motion with the defined amplitudes and phase differences of the horizontal and torsional motions. The vertical amplitude of the vertical–horizontal 2-DoF coupling oscillation can become very large if the horizontal amplitude increases and the phase difference between horizontal and vertical displacements approaches 180°. Meanwhile, the range of the stationary torsional angle in which the vertical–torsional 2-DoF coupling oscillation occurs becomes wide as the phase difference between the torsional and vertical displacements approaches 90°. However, without horizontal motion, the vertical amplitude has a limited value, even if the torsional amplitude becomes large.

被冰覆盖的输电线路上的风作用会导致飞驰，这是一个问题，因为它会导致相间短路并导致输电线塔和绝缘子的横臂疲劳。奔腾现象的特征是大振幅、低频的垂直、水平和扭转振荡的组合。为了更好地了解垂直、水平和扭转 3 自由度 (DoF) 在四束导体上疾驰的动态响应，对具有不同 DoF 和频率比的 2D 系统进行了时程分析。通过时程分析分析了导体非线性 1-DoF 垂直响应的基本特性，表明大的振荡是由包含具有高负升力系数斜率的相对攻角的角度范围引起的。通过考虑一个振荡周期内垂直运动的能量平衡，我们估计了稳定和不稳定的极限环振幅。然后，通过比较 1、2 和 3-DoF 系统的结果，我们阐明了空气动力耦合对 3-DoF 飞驰的影响。3-DoF 系统中的振荡类型根据固定扭转角分为垂直-水平 2-DoF 耦合振荡、垂直-扭转 2-DoF 耦合振荡和垂直 1-DoF 振荡。最后，我们通过考虑具有定义的水平和扭转运动的幅度和相位差的垂直运动的能量平衡来表明对垂直振荡的耦合效应。如果水平振幅增加并且水平和垂直位移之间的相位差接近 180°，则垂直-水平 2-DoF 耦合振荡的垂直振幅会变得非常大。同时，随着扭转位移和垂直位移之间的相位差接近 90°，发生垂直扭转 2-DoF 耦合振荡的固定扭转角的范围变宽。然而，如果没有水平运动，即使扭转幅度变大，垂直幅度也有一个有限的值。如果水平振幅增加并且水平和垂直位移之间的相位差接近 180°，则垂直-水平 2-DoF 耦合振荡的垂直振幅会变得非常大。同时，随着扭转位移和垂直位移之间的相位差接近 90°，发生垂直扭转 2-DoF 耦合振荡的固定扭转角的范围变宽。然而，如果没有水平运动，即使扭转幅度变大，垂直幅度也有一个有限的值。如果水平振幅增加并且水平和垂直位移之间的相位差接近 180°，则垂直-水平 2-DoF 耦合振荡的垂直振幅会变得非常大。同时，随着扭转位移和垂直位移之间的相位差接近 90°，发生垂直扭转 2-DoF 耦合振荡的固定扭转角的范围变宽。然而，如果没有水平运动，即使扭转幅度变大，垂直幅度也有一个有限的值。随着扭转位移和垂直位移之间的相位差接近 90°，发生垂直扭转 2-DoF 耦合振荡的固定扭转角的范围变宽。然而，如果没有水平运动，即使扭转幅度变大，垂直幅度也有一个有限的值。随着扭转位移和垂直位移之间的相位差接近 90°，发生垂直扭转 2-DoF 耦合振荡的固定扭转角的范围变宽。然而，如果没有水平运动，即使扭转幅度变大，垂直幅度也有一个有限的值。