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为研究机床的静刚度特性,需要得到其各部件的单元刚度矩阵。机床部件的结构往往是不规则的,因此需要将其等效简化为等截面梁单元,才能得到其单元刚度矩阵。该文对任意变截面梁等效简化为等截面梁单元的问题进行了研究,从建立梁单元的单元刚度矩阵的需要出发,推导出了完整的简化方法。为了验证该简化方法的有效性,利用有限元分析软件ABAQU S 6.51对一个力学模型进行了分析,同时用上述的简化方法对该力学模型进行了计算。将两者的计算结果进行对比,相对偏差小于5%,因此可证明该简化方法在变截面梁等效简化为等截面梁单元时的有效性。
In order to study the static stiffness characteristics of machine tools, we need to get the stiffness matrix of each component. The structure of machine tool parts is often irregular, so it needs to be simplified equivalently to the beam elements of the same section to get the stiffness matrix of the elements. In this paper, the problem of equivalently simplified variable cross-section beams into equivalent cross-section beam elements is studied. From the point of establishing the element stiffness matrix of beam elements, a complete and simplified method is deduced. In order to verify the effectiveness of the simplified method, a mechanical model was analyzed using the finite element analysis software ABAQU S 6.51 and the mechanical model was calculated using the simplified method described above. The results of the two methods are compared and their relative deviations are less than 5%. Therefore, it is proved that the simplified method is effective in reducing equivalent cross-section beams to equivalent cross-section beam elements.