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The herringbone gear power-split transmission is widely used in high-speed and heavy-load transmission systems, and its dynamic analysis is becoming increasingly important. The characteristic sensitivity of a gear transmission system indicates the influence of the dynamic parameters on the natural frequency of the gear transmission system, and it functions as an important theoretical reference value in the dynamic design of a herringbone gear power-split transmission system. In this paper, the dynamic equations of a herringbone gear power-split transmission system for a ship are presented, and the natural frequencies and modal shapes are calculated based on the free torsional vibration differential equation. Subsequently, the modal shapes were classified into the coupling vibration model and the branch vibration model. The characteristics sensitivity was studied using modal analysis, and the characteristics sensitivity calculation equations for single and double root of natural frequency were deduced, and the characteristic sensitivity of the natural frequencies to the mesh stiffness was computed. Finally, the relationship between the modal strain energy and the characteristic sensitivity was analyzed, and the physics essence of the characteristic sensitivity was revealed.

人字齿轮功率分流传动系统（herringbone gear power-split transmission）广泛应用于高速重载传动系统，其动力学分析的重要性日益凸显。齿轮传动系统的特性灵敏度（characteristic sensitivity）表征了各动力学参数对齿轮传动系统固有频率（natural frequency）的影响程度，可作为人字齿轮功率分流传动系统动力学设计的重要理论参考依据。本文首先建立了船舶用该类系统的动力学方程，基于自由扭转振动微分方程（free torsional vibration differential equation）求解了系统的固有频率与振型（modal shapes）；随后将振型划分为耦合振动模型（coupling vibration model）与分支振动模型（branch vibration model）。继而通过模态分析开展特性灵敏度研究，推导了固有频率单根与重根情况下的特性灵敏度计算公式，并计算了固有频率对啮合刚度（mesh stiffness）的特性灵敏度。最后分析了模态应变能（modal strain energy）与特性灵敏度之间的关联关系，揭示了特性灵敏度的物理本质。