直升机悬停状态下的振动计算

为降低直升机的共振危害,需要一种对直升机在空中悬停时振动特性快速计算方法.旋翼在离心力作用下,固有频率受应力刚化效应影响发生变化,同时存在旋翼桨叶/桨叶和旋翼/机身的耦合影响,动力学分析十分复杂,另一方面为提高计算效率,运动方程的低阶次、程式化成为迫切的需求.多体系统传递矩阵法(Transfer matrix method for multibody systems, MSTMM)同时解决了这两个问题.为准确快速计算悬停直升机固有频率,本研究基于MSTMM建立一种柔性四片旋翼与直升机机身耦合的动力学模型,推导出系统的动力学拓扑模型、总传递方程和特征方程.重点推导了空间旋转梁和旋转轴的传递矩阵,最终快速计算得出悬停直升机系统固有频率.研究表明:空间旋转梁MSTMM计算结果和ANSYS Workbench仿真结果对比,误差不超过2%,旋转轴MSTMM计算结果与参考文献结果基本一致;机尾固定的约束条件下,计算出36.651 9 rad/s转速下旋翼/机身耦合系统的前13阶固有频率,与ANSYS Workbench仿真结果一致,改为悬停无约束条件,计算得出悬停直升机系统前8阶固有频率,计算速度相较仿真速度提升了7.1倍,为直升机动力学分析提供一种新思路.

Calculation of helicopter vibration in hovering state

To reduce the resonance hazard of helicopters, a fast calculation method for the vibration characteristics of helicopters when hovering in the air is needed. Under the action of centrifugal force, the natural frequency of the rotor changes under the influence of the stress stiffening effect, and there are coupling effects of rotor blades/blades and rotors/fuselage at the same time, which makes the dynamics analysis complicated. On the other hand, in order to improve the calculation efficiency, the low-order and stylization of the kinetics equation has become an urgent need. The transfer matrix method for multibody systems (MSTMM) can solve these problems at the same time. In order to accurately and quickly calculate the natural frequencies of hovering helicopters, a dynamic model of the coupling between the four flexible rotors and the helicopter fuselage was established based on MSTMM, and the dynamic topology model, total transfer equation, and characteristic equation of the system were derived. The transfer matrix of the spatial rotating beam and spinning axis was derived in detail, and the natural frequency of the hovering helicopter system could be quickly calculated. The research shows that the error between the MSTMM calculation results and the ANSYS Workbench simulation results of the spatial rotating beam was not more than 2%, and the MSTMM calculation results of the spinning axis were basically consistent with those in literature. Under the constraints of fixed tail, the first 13 order natural frequencies of the rotor/fuselage coupling system were calculated at the speed of 36.651 9 rad/s, which were consistent with the simulation results of ANSYS Workbench. When the hovering was not restricted, the first eight order natural frequencies of the hovering helicopter system were calculated, and the calculation speed was increased 7.1 times compared with the simulation speed. The results provide a new idea for helicopter dynamics analysis.