复合材料多钉连接钉载分配均匀化的泰勒展开方法

A Taylor Expansion algorithm for the load distribution homogenization of multi-bolt composite joints

大多数复合材料机械连接都是多钉连接,但由于复合材料的脆性等因素,钉载分配往往极不均匀,极易引起接头的过早破坏.为改善钉载分配的不均匀性,工程中通常采用在承载较大的钉孔处设计间隙配合的方法,然而间隙量的大小一般难以确定.本文基于一阶泰勒展开方法提出一种确定该间隙的近似算法.首先将钉载关于钉孔间隙进行一阶泰勒展开,进而建立钉载和钉孔间隙之间的线性方程组.然后在指定外载荷条件下,以钉载均匀分配时的螺栓载荷为已知量,以钉孔间隙为未知量,计算各钉近似均匀分配时的钉孔间隙.以5钉连接接头为例,对模型有效性进行验证.结果表明,优化后,首钉钉载比例由45.1%降低到23.0%,首钉位置净截面的拉伸应力和压缩应力也有明显降低,较优化前分别下降26%和39%.最后基于验证的优化模型研究了宽度、排距、螺栓数目以及外载荷等参数的影响.模型分析效率高,对于n钉连接的多钉连接问题,只需n+1个有限元模型即可计算得到钉载近似均匀分配时的钉孔间隙.模型对复合材料多钉连接的均匀化设计具有重要的指导意义.

Most aircraft bolted joints consist of multiple bolts, and they may share the load unevenly due to the brittle nature of composites, which will easily lead to the premature failure of the joints. In order to decrease the bolt load inequality, the common method is to apply clearance fit at the most highly loaded bolt. However, it is always difficult to determine the clearance value. In this paper, a new method which is based on First Order Taylor Expansion was proposed to compute these values approximately. First, the First Order Taylor expansion was used to get the linear equation between the bolt load and the bolt-hole clearance. Then, under a given external load, using the bolt load when all the bolts share the load equally as the known parameters, and using the bolt-hole clearance as unknown parameters, a linear equation group is solved. The bolt-hole clearance was approximately calculated. The method was validated by applying it to a five-bolt joint. After optimization, the bolt load ratio of the most loaded bolt decreased from 45.1% to 23.0%. The maximum tensile stress and compressive stress of the joint decreased by about 26% and 39%, respectively. Finally, based on the validated model, the influence of parameters such as width, row spacing, number of bolts and external load was discussed. The model was highly efficient and for optimizing of an n-bolt joint, only n +1 finite element models were needed to obtain the desired clearance fit values. The model is of great significance for the optimization design of multi-bolt joints.