桥梁平转施工中球铰界面的摩擦力精确计算方法及验证

转体施工是桥梁施工中的重要方法，中国已成功将该技术应用于数百座大跨桥梁的施工。大吨位转体施工中，摩擦力的计算至关重要，但现有工程实践中给出的近似计算方法与工程试验值有较大差距。因此，精确的摩擦力和摩阻力矩计算理论，是转体施工中亟待解决的问题。首先采用称重原理获得竖向摩阻力矩，然后利用接触理论求得接触面的应力分布规律，并推导出竖向摩阻力矩理论公式，进而求得摩擦因数。之后，利用获得的摩擦因数，根据接触面的应力分布规律，获得了平转过程中的水平摩阻力矩和牵引力。最后，进一步将前述方法推广到带滑块的转体装置中，获得统一的摩擦因数、摩阻力矩计算方法。将该方法和有限单元法的计算结果进行对比，两者高度吻合；和实际工程数据对比，显示所提方法的结果更加合理、准确。主要结论如下：①根据称配重方法计算摩擦因数时，现有近似计算方法获得的摩擦因数，随着球铰参数α的增加误差逐渐增大。②球铰表面接触应力呈现出中间向两边逐渐增大的分布特征，现有计算方法假设均匀的法向接触应力分布与实际应力分布差距较大。无滑块转体装置中，有限元模型计算所得水平转动摩阻力矩比现有近似方法计算的大14.3%；而该方法计算值与有限元结果误差仅为3.0%。③在带滑块转体装置中，与工程实测值相比，现有近似方法和该改进方法获得的水平转动摩阻力矩误差分别为31.4%和23.7%。由此可见，该方法进一步提高了计算准确度。

Accurate Calculation Method and Verification for Friction Force of the Spherical Hinge Interface in Bridge Horizontal Rotation Construction

Rotation superstructure construction is an important method in bridge construction. This technology has been successfully applied to the construction of hundreds of large-span bridges in China. In large-tonnage rotation superstructure construction, the calculation of the friction force is of great importance, but the approximate calculation method given in the existing engineering practice has a large gap with measured values. Therefore, accurate theoretical calculation of the friction force and friction moment is an urgent problem in rotation superstructure construction. In this study, the principle of weighing was used to obtain the friction moment of vertical rotation. Then, contact theory was used to obtain the stress distribution of the contact surface, the theoretical formula for the friction moment of vertical rotation was derived, and the friction coefficient was obtained. Subsequently, using the friction coefficient already obtained, according to the stress distribution law of the contact surface, the friction moment of the horizontal rotation and the traction force during the horizontal rotation process were obtained. Finally, the method was further extended to a rotating mechanism with slide plates, and a unified calculation method for the friction coefficient and friction moment was obtained. The calculation results of this method were compared with the calculation results of the finite-element method, and the results were highly consistent. A comparison with actual engineering data showed that the results of the proposed method are more reasonable and accurate. The main conclusions are as follows. ① When calculating the friction coefficient according to the weighing and counterweight method, the error of the friction coefficient obtained by the existing approximate calculation method gradually increases with the increase in the spherical hinge parameter α. ② The contact stress on the surface of the spherical hinge shows a distribution characteristic that gradually increases from the middle to both sides, and the existing calculation method assumes that the uniform normal contact stress distribution is far from the actual stress distribution. In the rotating mechanism without slide plates, the friction moment of horizontal rotation calculated by the finite-element model is 14.3% larger than that calculated by the existing approximate method, but the error between the calculated value of the method in this study and the finite-element result is only 3.0%. ③ In the rotating mechanism with slide plates, compared with the measured value of engineering, the errors for the friction moment of horizontal rotation obtained by the existing approximate method and the improved method in this study are 31.4% and 23.7%, respectively. It can be seen that the method used in this study further improves the calculation accuracy.