Torque and Friction Coefficient Analysis

In the realm of bolted connections, the torque coefficient K plays a pivotal role, visually revealing the relationship between the tightening torque of a bolt and the resulting clamping force. The torque coefficient K not only has a decisive influence on the torque magnitude during on-site bolt installation but also provides a simple method for converting torque to clamping force. However, when attempting to comprehensively explore the moment conversion and consumption during the bolt tightening process, relying solely on the torque coefficient K seems overly simplistic, as it is a synthesis of multiple variables. To deeply understand the impact of individual variables such as geometry and friction on bolt performance, we must introduce another key parameter—the friction coefficient μ.

Researchers at the Wright-Patterson Air Force Base in the United States identified a series of factors affecting the relationship between bolt torque and preload years ago. These factors include the material of the bolt, forming process, thread shape, concentricity, as well as the hardness of the thread connection pair and washers. Additionally, the type of washer, surface roughness of the component, burrs on the internal thread edges, thickness and type of bolt coating, and even the lubrication of the bolt, tightening tool, speed, number of uses, and ambient temperature are all on this list of influencing factors.

It is noteworthy that most of these factors are closely related to friction. Friction has a significant impact on the preload of high-strength bolts. As shown in Figure 1, more than 80% of the torque applied to high-strength bolts is used to overcome frictional forces. This finding highlights the importance of the friction coefficient in the distribution of preload within the tightening torque.
Through testing results, we found that under the same tightening torque, a slight change in the friction coefficient (0.01) can lead to a preload variation of up to 37.5%. Further analysis of the torque conversion distribution in Figure 1 reveals that 50% of the applied torque is consumed by the friction at the supporting surface, 40% by the thread friction, and only 10% is converted into preload.

If the friction between the supporting surfaces increases by 10% due to a slight increase in surface roughness, the torque consumption at the supporting surface would increase from 50% to 55%, with this additional 5% not affecting the friction between threads but instead reducing the preload from 10% to 5% of the total preload torque. This means that the final preload of so-called "problem bolts" is only half that of ordinary bolts. It is evident that a 10% increase in friction force can lead to a 50% change in preload, hence the research on the thread pair friction coefficient must be taken very seriously.

In our country's design standards, the relationship between tightening torque, axial force, and friction coefficient has been explicitly stated. The relevant formulas in the "China Mechanical Design Encyclopedia (Volume 3)" indicate that pitch and friction coefficient are key factors affecting the ratio of tightening torque to axial force, which aligns with our analysis of the factors influencing the torque coefficient K.

In Europe, particularly in Germany, the control of the friction coefficient μ during the testing and tightening of high-strength bolts is given special attention. This is evident from European wind power technology drawings, which typically specify the friction coefficient rather than the torque coefficient. Since the testing equipment for the thread pair friction coefficient mainly comes from Europe, especially Germany, the test reports also adopt the European convention for symbol representation.

Through the analysis of testing data, we found that to ensure the stability of the K-value and to ensure that the axial force is within the design range and uniform, we need to pay more attention to the thread friction coefficient. In the actual bolt tightening process, to ensure the consistency of the thread friction coefficient, it is recommended to apply lubricant to the bolt using a scraping and coating process.

Research also shows that when bolts become loose, it is usually the thread engagement area that loosens first, followed by sliding at the supporting surface. This indicates that under the same surface condition, thread friction is the weaker link. Therefore, when considering anti-loosening measures, we should also focus on the thread friction coefficient.

The magnitude of the friction coefficient directly affects the proportion of tightening torque converted into preload. A friction coefficient that is too high can lead to excessive tightening torque, increasing tool wear and operational risk; a friction coefficient that is too low may cause the preload to be overly sensitive to the tightening torque, easily leading to overloading. Therefore, finding an appropriate range for the friction coefficient is crucial. According to German experience, the recommended range for the friction coefficient is 0.07 to 0.12. Within this range, the thread friction coefficient, supporting surface friction coefficient, and total friction coefficient are considered suitable and reliable.