Novel Modeling and Vibration Analysis Method on a Helicopter Drive Train System

When it comes to analyzing the dynamic characteristics of a geared system, it is common practice to create an equivalent mathematical model for which the rotational velocity is the same for all the elements. In contrast to creating the equivalent system firstly, a novel strategy based on the transfer matrix method is developed, which can directly obtain the equation of motion according to the system topology figure. Actually, any kind of topology of the system, e.g., geared branch or geared closed-loop systems, can be decoupled into a combination of a series of independent chain systems via introducing the virtual branched-gear transfer matrix. The overall transfer equation of the system can be efficiently obtained because the transfer matrix method of a chain system is simply matrix multiplication. The transfer matrices of typical gear types, e.g., reduction gear and planetary gear, are derived. In particular, a simple and aesthetic transfer matrix of rotating beam is derived to solve the rotor blade flapping or lead-lag vibration problems. A dimension reduction strategy is also introduced to address the dimension unmatched issue, further reducing the scale of the overall transfer matrix of the system. At last, an application on modeling an analysis of the coupled flexible rotor blade/engine/tail rotor/drive train system of a helicopter is presented.