对1.5 MW风力发电机齿轮箱传动系统进行耦合振动分析，建立了风力机增速箱齿轮传动系统的扭转振动模型。利用4阶RungeKutta法计算了系统在风载、轮齿时变啮合刚度和系统阻尼共同作用下的动态响应，并利用谐波平衡法求出了系统的解析解，从而得到了优化设计目标函数的解析表达式。在此基础上，建立了以行星轮扭转振动加速度幅值最小和传动系统总质量最轻为目标的优化设计数学模型，利用MATLAB优化工具箱进行优化求解。实例计算表明，优化设计后传动系统的低阶固有频率明显提高，动态性能明显改善，重量减轻。

Through coupling vibration analysis of the transmission system of a 1.5 MW wind turbine gearbox, a torsional vibration model of a gear drive system in wind turbines is established. The fourthorder RungeKutta integration method is applied to calculate the dynamic response of a gear system caused by wind loads, timevarying meshing stiffness, and system damping. The harmonic balance method is used to find the analytic solution. Based on the solution, a mathematical model for optimum gear system design is established. The model aims at minimizing the vibration acceleration of the planet gear and the total mass of the gear transmission system. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A calculated example shows that the primary natural frequency of the gear system has been raised, the dynamic properties of the gear train have been improved remarkably, and the total mass of the gear train has been decreased.

国家自然科学基金资助项目(50675231)；国家“十一五”科技支撑计划资助项目(2006BAF01B0701)