基于向量式有限元法的风力发电机组一体化仿真分析

大型风电机组为强非线性刚柔耦合的周期时变多体系统,传统有限元方法不能解决叶片转动过程中由于刚体位移而导致的刚度矩阵奇异问题,向量式有限元法可有效考虑叶片的几何非线性和大变形运动、塔架的弹性变形、气动载荷等因素.基于MATLAB平台编制空间梁系结构求解程序,选取悬臂梁受端部集中动荷载和欧拉梁绕定轴转动两个典型算例验证程序的正确性.建立包含机舱、轮毂、叶片和塔架在内的风电机组一体化仿真分析模型,根据机组静止状态下自由振动响应,用模态参数识别方法提取了机组的自振频率,计算结果与传统有限元法吻合.采用谐波叠加法和本征正交分解法相结合的方式,运用B样条曲面插值策略,模拟生成风电机组在正常运行状态下的风速时程.采用向量式有限元法对正常运行状态下的风电机组进行风振响应分析,较好地反映了重力对叶片内力周期性变化的影响以及叶片与塔架的共同作用.

Integrated Simulation of Wind Turbine Based on Vector Form Intrinsic Finite Element

Large wind turbine system is a periodic time-varying system with rigid-flexible coupling multi-bodies. The traditional finite element method cannot solve the singular stiffness matrix produced by the rotation of blades. However, the vector form intrinsic finite element method can effectively solve the geometric deformation of elastic continuum, the nonlinear or discrete constitutive model, the coupling motion of continuum and rigid body, and so on. In this study, a solver program of space beam elements was developed by the vector form intrinsic finite element method with MATLAB code, and verified by two typical examples where one is a cantilever method with a dynamic force acting at the end, and the other is an Euler beam rotating around a fixed axis. The integrated simulation of wind turbine system that consists of tower, rotor blades, and nacelle was then established, and its dynamic response of free vibration under parking was analyzed. The natural frequencies of the turbine system were obtained by modal parameter identification, and they agree well with the results obtained by traditional finite element method. Moreover, the weighted amplitude wave superposition method and proper orthogonal decomposition method as well as B-spline surface interpolation were employed to obtain the wind time series of wind turbine under the normal operation condition. The wind-induced dynamic response of wind turbine system was also calculated by vector form intrinsic finite element method. The results reflect the periodic influence of gravity on the internal forces of blades and the interaction between blades and the tower.