Abstract:  It was difficult to accurately determine the thread stresses on the bolts under pre-tensionsing conditions， which might lead to strength fracture and premature loosening of the threads， and the reliability of the bolt joints was compromised. Currently， the contact state of the thread surfaces was usually described by stresses under an absolute coordinate system. However， the simulated stress direction was at an angle to the actual thread surface. The analysis results were not intuitive. Therefore， a thread mathematical model was derived and the extended stress analysis method of thread contact surfaces was proposed. Then， the finite element model of bolt joints was established for the structural characteristics of bolts. And the accuracy of the model was verified by tests. Finally， the extended stress analysis method was applied to study the thread surface stress and the distribution characteristics of bolts. The results show that the maximum error between the simulated preload and the testing preload is only 5.78%, where the accuracy of the simulation model is demonstrated. The extension stress analysis method may reflect the continuity and monotonicity of the stress distribution on the thread surfaces, and the method also reflects the optimal preload. The decreasing rate of the stress on the same layer thread is inversely proportional to the stress. From the stress analysis， the reason why the stresses on the thread are mainly concentrated in the first three turns is illustrated. The thread extension stress analysis method proposed herein is more intuitive and accurate. The paper may provide theoretical support for the anti-loosening analysis and reliability analysis of bolts.

Key words: preload, bolt joint, thread, mathematical modeling of threaded surface, stress distribution

摘要： 螺栓在预紧状态下的螺纹受力情况无法准确判断，可能引发螺纹的强度破坏和过早松动，进而影响螺栓连接的可靠性。螺纹面接触状态通常采用绝对坐标系下的应力进行描述，而有限元计算应力方向与实际螺纹面存在一定角度，导致分析结果不直观。为此，推导了螺纹面数学表达式，并提出了螺纹接触面扩展应力分析法；然后针对螺栓连接结构特点建立了螺栓连接有限元模型，并通过试验验证了模型的准确性；最后应用扩展应力分析法研究了螺栓在预紧状态下的螺纹面应力及其分布特点。研究结果表明，仿真预紧力与试验预紧力的最大误差仅为5.78%，证明了仿真模型的准确性；扩展应力分析法能够反映螺纹面应力分布的连续性和单调性，且能体现最优预紧力的存在；同圈层螺纹面上的应力下降速率与应力大小成反比，从受力分析角度说明了螺纹牙上的应力主要集中在前三圈的原因。提出的螺纹扩展应力分析法使螺纹接触面受力分析更加直观、准确，研究结论可为螺栓连接结构防松分析与可靠性分析提供理论支撑。

关键词: 预紧力, 螺栓连接, 螺纹, 螺纹面数学模型, 应力分布