计算叶片力学特性的三维8节点非协调有限单元法

Three-Dimensional 8-node Incompatible Finite Element Method forCalculating Mechanical Properties of Rotor Blades

针对叶片结构几何形状复杂的特点 ,建立了能进行叶片力学特性分析的三维 8节点非协调有限单元模型。该模型采用了几何非线性和线弹性模式 ,来考虑叶片径向刚度远大于弯曲刚度而引起的在不同转速下初应力对叶片的作用 ,能够正确反映叶片的弯曲和扭转耦合振动模态、叶片组的切向和轴向振动模态以及它的应力状态。根据质量等效和力等效的原理 ,导出了在非协调单元中计算单元变形能时 ,记入附加的内部自由度 ,而计算单元的动能、体积力、表面力、以及阻尼力所做的虚功时 ,不记入附加的内部自由度 ,这是不同于目前一些文献中的提法。最后 ,通过实例计算验证了该模型的正确性。

Three dimensional 8-node incompatible finite element model for calculating static and dynamic characteristics of rotor blades is presented in accordance with the complicated geometry of blades with profile twist, taper and lean. Large displacement but small strain condition and Green-Lagrange strain formulation are employed to take into account the effect of pre-stress due to rotation for blade structure with bending stiffness very small compared with radial stiffness. The model can describe the coupled bending and twisting vibratory mode of blades, axial and tangential vibratory modes of group blades and stress distribution in blades. Based on mass equivalence and force equivalence, conceptions are obtained that the additional inner degrees of freedom should be considered for calculating element strain energy, whereas the additional inner degrees of freedom couldn't be considered for calculating kinetic energy, works done by body, frictional damping and surface forces. The concepts are different from that in some literatures. For illustration purpose, vibration analysis of 4-blade groups at rated speed and 19-blade long span cover blade groups at still are made using the proposed model. The predicted results agree well with the measured results when blades are assembled in real rotors.