螺栓与被连接件间轴向相对刚度的修正计算

螺栓连接结构的载荷分配比例和螺栓与被连接件间的轴向相对刚度密切相关。为了更准确地求解螺栓连接结构中螺栓与被连接件间的轴向相对刚度，基于被连接件垂直于螺栓轴的各受压层压应力均匀分布与非均匀分布形式下的轴向压缩变形量解析式，结合有限元仿真结果，提出了被连接件压缩变形体起始直径的修正公式及轴向压缩变形量的修正解析式。通过提取仿真应力值，对压应力理论修正方程、压应力仿真拟合方程进行积分计算。对比计算结果发现：用仿真拟合方程计算得到的被连接件压缩变形体轴向压缩变形量与用理论修正方程计算得到的变形量的误差小于2.5%，这说明用仿真拟合方程求解被连接件压缩变形体的轴向压缩变形量具有较高的精度。研究结果表明：修正起始直径与夹紧长度、螺栓头与螺母支承面直径呈线性关系。压应力非均匀分布下，用被连接件压缩变形体轴向压缩变形量的修正解析式求解螺栓与被连接件间轴向相对刚度时，误差小于2%，表明该修正解析式能够较为准确地计算螺栓与被连接件间的轴向相对刚度。在修正起始直径的基础上，基于被连接件各受压层压应力非均匀分布的轴向相对刚度计算结果比基于均匀分布的更准确。研究结果为理论研究和实际工程中准确分析螺栓的受力情况提供了一定参考。

Modified calculation of axial relative stiffness between bolt and connected parts

The load distribution ratio of the bolted joint structure is closely related to the axial relative stiffness between the bolt and the connected parts. In order to more accurately calculate the axial relative stiffness of the bolt and the connected parts of bolted joint structure, according to the analytical formula of axial compression deformation based on uniform and non-uniform distribution of compressive stress in each compressed layer of connected parts perpendicular to bolt axis,and combined with the finite element simulation results, the initial diameter modified formula and the axial compression deformation modified analytical formula for the compression deformation body of connected parts were proposed. By extracting simulated stress values, the integral calculation for theoretical modified equation and the simulated fitting equation of compressive stress was carried out. By comparing the computation results, it was found that the errors of the axial compressive deformation of the compression deformation body of connected parts calculated by the simulated fitting equation and the theoretical modified equation were less than 2.5%. It was shown that the accuracy of solving the axial compressive deformation of the compression deformation body of connected parts by simulated fitting equation was high. The results showed that the modified initial diameter was linear with the clamping length and the diameter of bearing surface between bolt head and nut. Under the non-uniform distribution of compressive stress, the errors of calculating the axial relative stiffness between the bolt and connected parts by using the modified analytical formulas of the axial compressive deformation of compression deformation body of connected parts were less than 2%, which indicated that the modified analytical formulas could calculate the axial relative stiffness between the bolt and connected parts more accurately. On the basis of the modified initial diameter, the calculation results of the axial relative stiffness based on the non-uniform distribution of compressive stress were more accurate than that based on the uniform distribution. The research results provide reference for accurately analyzing the force of bolts in the theoretical research and actual engineering.