The torque factor reflects the relationship between the axial preload of the bolt and the tightening torque. For high-strength bolted connections that are widely used in important applications such as automobiles, aviation, railways, petrochemicals, nuclear power, bridges and steel structures, the bolt pre-tightening force must be accurately controlled to ensure the safety and reliability of the joint structure. Improper preload will cause damage to the connection structure. If the bolt pre-tightening force is too large, the bolt may be broken, the connected parts may be crushed, bitten, twisted or broken, or the thread may be cut and tripped; the bolt pre-tightening force is insufficient, and the joint is slipped. , separation or loose fasteners, reducing the fatigue life of the bolt. Once the bolt connection fails, it will have serious consequences. On June 29, 2010, the "Space Trek" game cabin equipment in the East China Sea of â€‹â€‹Shenzhen City suffered from the sudden failure of bolts, causing the tragedy of 48 tourists and 6 deaths and 10 injuries. Controlling the pre-tightening force by controlling the tightening torque is a commonly used method in engineering practice. There are many factors affecting the change of bolt torque coefficient. Carrying out research in this aspect, trying to reduce the torque coefficient value and improve its stability is of great significance for ensuring the safe operation of bolted joints.
1 Concept and theoretical analysis of torque coefficient
The general structure of the bolted joint is shown in Figure 1. Due to the tightening torque T, an axial preload force F is generated between the threaded connecting piece and the connected piece. If the nominal diameter of the thread is d, the coefficient K is defined.
Where K is the bolt torque factor, which reflects the relationship between the tightening torque of the bolted joint and the preload. According to the mechanical model analysis in , it can be further derived.
Where p is the thread pitch, Î² is the thread half angle, r2 is the thread diameter, rn is the equivalent friction radius between the nut and the support surface, Î¼b is the thread friction coefficient, and Î¼n is the coefficient of friction between the nut and the support surface. .
As seen from equation (2), the torque factor K contains two sets of variables, one is the friction coefficient variable and the other is the geometric parameter variable of the thread. For a specific bolted joint structure, due to the instability of the friction coefficient and the difficulty in determining the size in advance, although there is a theoretical formula for calculating the torque coefficient K value, the theoretical calculation cannot be obtained, and a specific bolt connection is made. The thread geometry parameter variable will also change during the pre-tightening process. At present, most of the mechanical design manuals and related textbooks in China give the recommended values â€‹â€‹of the torque coefficient, which are selected by the designer or the user according to the conditions of use . Lu Wei et al.  calculated and comprehensively analyzed the standard coarse-tooth bolts of 12 sizes in the range of M12-M48 according to the relationship between friction coefficient and torque coefficient, and gave a simple relationship between the torque coefficient K value and the friction coefficient. Correspondence calculation formula.
2 Experimental study on factors affecting torque coefficient
Through the theoretical analysis of the torque coefficient value of the bolt, it can be seen that all the factors affecting the change of the friction coefficient of the thread and the support surface and the change of the geometrical parameters of the thread will affect the torque coefficient. Many researchers have carried out experimental research on the factors affecting the torque coefficient and achieved certain results. Yanyao Jiang et al.  studied the effects of materials, surface treatment, repeated tightening, tightening speed and other factors on the torque coefficient K of the bolt. The dispersion rate of K value comprehensively reflects the influence degree of each factor. Sayed A. Nassar et al. [5-7] studied the effects of tightening speed, repeated tightening and loosening, surface coating type and thickness on the coefficient of friction of the thread and the friction coefficient of the bearing surface of the nut. The results show that increasing the thickness of the coating can reduce the friction coefficient. , reduce the torque factor K value. Zou et al.  studied the effects of three lubricants, such as lubricating oil, grease and solid film, on the friction coefficient and torque coefficient. Cao et al.  studied the effects of lubrication conditions, support surface chattering and surface treatment conditions on the torque coefficient of aviation bolts. Xiong Yunqi et al.  studied the relationship between friction coefficient and torque coefficient of automotive fasteners. However, the above experimental studies were carried out in an indoor environment in which the bolting environment was applied.
When the bolting environment is different from the indoor environment, the change of the temperature and humidity will greatly change the bolt torque coefficient, especially for the high-strength bolt connection structure. Liang Jianhua  studied the variation law of bolt torque coefficient with the specification of M25Ã—100 in the range of 13ï½ž27 Â°C. The results show that the torque coefficient changes by about K=-6.6 Ã—10- for every 1 Â°C increase in temperature. 4 / Â° C, the average rate of change was 0.49 / Â° C. Fang Wan et al  studied the effect of temperature changes on the tightening of high-strength bolts, indicating that the increase in temperature will result in a reduction in the torque factor. Yu Xiang et al.  studied the torque coefficient of high-strength bolts on temperature factors. The results show that as the temperature decreases, the K value of the torque coefficient increases; when the temperature rises, the K value decreases. Shen Jiaxuan et al.  studied the effect of changes in ambient temperature on the torque coefficient of high-strength bolts. The temperature difference is 10 Â°C, and the torque coefficient will vary by 6% to 7%. Wang Junfeng et al  obtained the influence of temperature and humidity on the bolt torque coefficient of phosphating and phosphorus saponification. The effect of temperature on the torque coefficient of high strength bolts after surface treatment showed the same change law. The torque coefficient decreases with the increase of temperature; while the humidity changes the torque coefficient of the bolt obtained by the two treatments, the torque coefficient of the phosphating bolt increases with the increase of the humidity, while the torque coefficient of the phosphorus saponified bolt is It decreases with increasing humidity, and the torque coefficient drops sharply when the humidity is greater than 90%. Ma Yongxing  studied the change of torque coefficient of high-strength bolts in the temperature range of -6 ~ 6 Â°C and constant humidity. The results show that the torque coefficient increases by 3% in the range of -3 to 0 Â°C. The torque factor increases by 5% in the range of 6 to -3 Â°C.
3 bolt torque coefficient application
The magnitude and variation of the torque coefficient have important guiding significance for the design, manufacture and installation of bolted joints. For example: 1 When designing, the pre-tightening force is the basic data in the design calculation. It is necessary to accurately know the torque coefficient value to conveniently indicate the torque control value in the design pattern. 2 When manufacturing, select the reasonable surface treatment by improving the bolt production process. Ways, strengthen the quality assurance system, improve the precision of thread manufacturing, reduce the torque coefficient value and improve its relative stability; 3 When assembling, the speed of bolt tightening and the number of cyclic tightening should be strictly controlled, and the bolts that have not been used for a long time should be tightened. Grease is applied during the process to reduce the torque factor value.
There are many factors affecting the change of the torque coefficient value, and the friction coefficient of the thread surface and the support surface determines the magnitude of the torque coefficient. Research on the factors affecting the bolt torque coefficient should try to reduce the torque coefficient value and improve its relative stability. From the open literature, there are many studies on the influence of the parameters, materials, surface state, lubrication conditions, tightening speed and repeated tightening of the thread fasteners on the torque coefficient at home and abroad, and the impact on the ambient temperature and humidity factors. Less research, especially on negative temperature or high humidity environments. Strengthen the research on the correlation between bolt torque coefficient and ambient temperature and humidity. For outdoor high-strength bolt connection devices with large difference between construction environment and indoor environment, it can provide accurate data and guidance for bolt screwing, and reduce on-site re-inspection of bolt torque coefficient. To maximize the safety and reliability of major bolted connections.
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