复约束方法计算斜齿圆柱齿轮结构特征值问题

根据齿轮结构的循环对称性，以仅含有一个完整轮齿的扇形子结构作为齿轮有限元计算模型，用计算循环对称结构特征值问题的复约束方法，通过求解一个扇形子结构的特征值问题得到整个齿轮结构的特征值和特征向量。计算了４个不同参数齿轮的低阶固有频率和振型，并与实验结构数据比较，获得了满意的结果。这证明复约束法既极大地减少了计算所需内存和机时，又可建立包含轮齿和轮体在内的计算模型，保证了齿轮结构特征值问题计算的完整性和准确性。

CALCULATION OF EIGENPROBLEMS OF HELICAL GEAR STRUCTURE BY COMPLEX CONSTRAINT METHOD

Owing to its cyclic symmetry the complex constraint method for the eigenproblems of cyclic symmetric structure is applied to calculating the eigenpairs of the helical gear structure.The method chooses a sector substructure including only one gear teeth as finite element calculating model.The cyclic symmetric conditions of node points are presented to modify the stiffness and mass matrices of the substructure.With the use of the structural cyclic symmetry and the complex constraint conditions,the eigenvalue equations of the whole gear structure are uncoupled.All eigenvalues and eigenvectors of the whole gear structure can be obtained from calculating the eigenproblems of the sector substructure.The first several natural frequencies and the corresponding model shapes of four helical gear structures with different parameters are evaluated.The calculated results are in good agreement with experimental data.