What is the torque coefficient K for wind power bolts?

There is a relationship between the tightening torque T applied to a bolt and the axial force F as follows:

T = K • D • F

Where D is the nominal diameter of the bolt, and K is known as the torque coefficient. The torque coefficient K is a constant determined by experimentation. Its value depends on the geometric shape of the thread pair and the frictional conditions between the threads. From the formula, it can be seen that the torque coefficient K determines the proportion of axial force in the conversion of tightening torque, making this coefficient very important for the study of bolt fastening.

Firstly, the geometric shape of the fastener determines how much tightening torque can produce a specific preload force. Here, the pitch is a decisive factor. A bolt is a geometric body that is equivalent to a "spiral rising plane," which affects the distribution of forces in the entire threaded connection (10 Steps to Reliable Bolt Assembly, by Dr. Volker Schatz, P13). Since this geometric shape depends on the bolt manufacturer, we will not analyze it here.

The second influencing factor is the frictional condition. Any factor that can change friction can affect the torque coefficient K. For example, whether there is a lubricant on the bolt surface, and if a lubricant is chosen, the type of lubricant and the specific application process will also affect the coefficient K.

With different frictional conditions on the thread surfaces, the converted preload force will also differ. The better the lubrication conditions of the bolt, the greater the preload force under the same preload torque, meaning the smaller the torque coefficient K. What we need during the tightening process is a stable and moderate preload force, which requires a stable torque coefficient K to ensure the uniformity of preload force on the same flange surface. Under the same tightening torque T, if the K value is too large, the converted preload force will be too small to meet the design requirements; if the K value is too small, it will amplify errors, and due to systematic errors in the entire operation and monitoring, such as a torque wrench having an error of ±4%, it can easily lead to axial force overload and failure of the threaded connection; if the K value is unstable, the converted preload force will be inconsistent, easily leading to stress concentration. The use of lubricants can greatly improve the stability and consistency of the bolt torque coefficient, effectively avoiding these risks, which is why the wind power industry widely uses anti-seizing lubricants for bolts with higher torque requirements.

In specific construction, different application methods can have a significant impact on the final lubrication effect, which is reflected in the change of the torque coefficient K. Currently, in the wind power industry, there are two common methods for applying anti-seizing agents to high-strength bolts:

Apply lubricant only to the thread engagement area, i.e., the threaded engagement area of the bolt, as indicated by point A in Figure 1. This method results in a torque coefficient between 0.11 and 0.15, depending on the type of lubricant and bolt.

Apply lubricant not only to the thread engagement area but also to the supporting surface, i.e., the contact area between the lower end of the bolt head and the washer (for processes where torque is applied to the bolt head, if torque is applied to the nut, then it is the contact surface between the nut and the washer), as indicated by point B in Figure 1. This method results in a torque coefficient between 0.08 and 0.13. (Influencing Factors of High-Strength Bolt Torque Coefficient, "Fasteners," April 2010, Issue 21, P135, Shanghai Shenguang High-Strength Bolt Co., Ltd., by Sun Xinhua and Zhang Xianming).

Regarding the torque consumption for tightening high-strength bolts, the above figure has visually expressed this. For method 1, it is equivalent to reducing the friction at area A. However, we note that the friction at area B accounts for nearly 50%. If no lubrication measures are applied to this area, the final converted clamping force will be greatly influenced by area B, resulting in significant fluctuations in the bolt torque coefficient and standard deviation easily exceeding the acceptable range. Conversely, if the anti-seizing lubricant is applied to area B as well as area A, the final torque coefficient fluctuations will be smaller, the standard deviation will be minimal, and the wind power system will operate more reliably.

Two years ago, many domestic wind power companies were still using method 1. After conducting a large number of comparative experiments, several leading domestic wind power companies have reformed their bolt lubrication processes in the past year and adopted method 2, mainly to eliminate factors affecting the instability of the torque coefficient, to achieve good consistency of the torque coefficient, and to ultimately obtain a uniform clamping force.

However, since method 2 involves lubricating the end surface, the resulting torque coefficient is between 0.08 and 0.13, meaning the friction of the thread pair is reduced. Could this cause the bolt to become loose more easily? Let's take another look at another coefficient – the friction coefficient.

The friction coefficient is a key factor that affects the torque coefficient. When the friction coefficient is reduced, the torque coefficient also tends to decrease. In the case of method 2, although the friction at the end surface (B area) is reduced, the application of anti-galling lubricants can ensure a more consistent and reliable clamping force. This is because the lubricant helps to stabilize the friction conditions, resulting in a smaller fluctuation of the torque coefficient and a lower standard deviation, which in turn leads to a more reliable operation of the wind power system.

However, the concern about the bolt becoming loose due to reduced friction is valid. To address this, it is crucial to select the right type and amount of lubricant, and to apply it correctly. The lubricant should provide enough friction to prevent the bolt from loosening under operational vibrations and loads, while still allowing for a consistent torque coefficient.

In summary, the choice of lubrication method for high-strength bolts in wind power applications is a balance between achieving a consistent torque coefficient and ensuring the bolt's clamping force remains secure over time. Proper selection and application of lubricants, along with rigorous testing and quality control, are essential to the reliable operation of wind turbines.0.08 and 0.13, meaning the friction of the thread pair is reduced. Could this cause the bolt to become loose more easily? Let's take another look at another coefficient – the friction coefficient.

The friction coefficient is a key factor that affects the torque coefficient. When the friction coefficient is reduced, the torque coefficient also tends to decrease. In the case of method 2, although the friction at the end surface (B area) is reduced, the application of anti-galling lubricants can ensure a more consistent and reliable clamping force. This is because the lubricant helps to stabilize the friction conditions, resulting in a smaller fluctuation of the torque coefficient and a lower standard deviation, which in turn leads to a more reliable operation of the wind power system.

However, the concern about the bolt becoming loose due to reduced friction is valid. To address this, it is crucial to select the right type and amount of lubricant, and to apply it correctly. The lubricant should provide enough friction to prevent the bolt from loosening under operational vibrations and loads, while still allowing for a consistent torque coefficient.

In summary, the choice of lubrication method for high-strength bolts in wind power applications is a balance between achieving a consistent torque coefficient and ensuring the bolt's clamping force remains secure over time. Proper selection and application of lubricants, along with rigorous testing and quality control, are essential to the reliable operation of wind turbines.