基于模态理论的白车身静刚度计算方法

A Calculation Method of Car Body in White's Static Stiffness Based on Modal Theory

以线性系统的模态理论为基础,将简单矩形框架的弹性体模态与静刚度之间的关联性推广到白车身,推导出了具体的数学表达式,再以此为依据,通过有限元分析直接提取各阶弹性体模态参数,从而获取车身静刚度,改变了以往依靠柔度矩阵和大型试验来计算静刚度的方法。研究结果表明,模态理论方法和传统静力学方法所得到的静刚度相差在10%以内,说明白车身的整体静态柔度可以用模态柔度贡献量之和表达,且这种计算方法具有较高精度,能为低阶模态和刚度性能的目标设定提供参考。同时,各阶模态的柔度贡献量的大小可以作为低阶模态识别的重要依据。最后将有限元计算结果与白车身静刚度试验结果作对比,其误差控制在8%以内,其中由模态方法计算的扭转刚度误差低于3%,因此说明此次有限元分析是可靠的。

The mathematical relationship of simple rectangular frames between flexible modes and static stiffness were generalized to car body in white based on the modal theory in linear systems,and the specific mathematical expressions for stiffness calculation were derived.The modal method which obtained static stiffness by extracting each modal parameters with FEA was described,instead of the previous methods of calculating static stiffness based on the compliance matrix theory and large tests.The results show that,the differences of static stiffness values calculated by two methods respectively are less than 10%,which illustrates that the global static compliance of the car body may be expressed by the sum of all modal compliance contributions,and this calculation method has high precision,so it may provide a reference for target setting of low order modes and stiffness properties.Furthermore,the modal compliance contributions may be an important basis for modal identification.Finally,comparing the finite element calculation results and static stiffness test ones,the errors are less than 8%,especially the torsional stiffness calculation errors are less than 3%,which are calculated by the modal method.So it illustrates that the FEA is reliable.