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Mechanism analysis of bolt fastening

March 27, 2024

The essence of torque control

The fundamental purpose of threaded connections, especially important threaded connections that bear dynamic loads, is to use threaded fasteners to reliably connect the connected parts together. The essence of assembly tightening or assembly torque control is to control the axial preload of the bolt within an appropriate range. The bolt is inserted into the connected part, and the bolt is stretched and deformed by tightening the nut or internal thread. This elastic deformation produces an axial pulling force, which squeeches the clamping part together, known as the pre-tightening force. Theoretically speaking, the greater the axial preloading force, the better the anti-loosening and anti-fatigue performance, and the best effect is when the preloading force reaches or is close to the yield strength of the bolt.


Relationship between preload and torque
The torque method is to control the axial preload indirectly by controlling the assembly tightening torque. The following basic relationship exists between the tightening torque M of the bolt and the axial preload F of the bolt:
Where M - tightening torque, K - torque coefficient, F= pre-tightening force, D is the nominal diameter of thread.
In the empirical design, the torque coefficient K value is generally 0.2, but in reality, the K value is not a constant, but a variable that depends on other conditions such as thread accuracy. Under the general batch assembly conditions, according to the thread accuracy, material, surface state and lubrication conditions, the K value of the same connection can be in 0.1-0.5 or even wider range change, generally, the higher the thread manufacturing accuracy, the more stable the surface treatment and lubrication conditions, the more stable the K value (small dispersion), on the contrary, the larger the dispersion.


When considering the divergence of the K value, in order to meet the design requirements of the preload force, the upper and lower limits of the bolt tightening torque can be determined by the following formula:

FU, FL -- upper and lower limits of axial preload required by design;
KU, KL -- upper and lower limits of K value under specific process conditions;
The above formula shows that after the design of the thread connection (thread diameter D and axial force FU, FL) is determined, the greater the divergence of K value, the stricter the control of the assembly torque (the smaller the Mu-ML). Similarly, when the torque control accuracy (Mu, ML) is determined, the greater the dispersion of the K value, the more dispersed the axial force and the worse the reliability of the threaded connection.


Relationship between preload force and Angle of rotation
When the fastener is rotated during tightening, what is the relationship between the preloading force and the Angle of the fastener?
From the kinematics of the thread and the analysis of the force state of the fastener and the connected part, it can be seen that in the beginning stage of screwing the bolt or nut, the corner will not produce pretension force, only when the end of the connector contacts the connected part, the pretension force begins to produce, and only when the complete fit, F and θ are wired, the basic relationship between the pretension force and the corner is as follows:
F = CPθ
(F - preload force, C composite stiffness coefficient, P pitch, θ bolt head rotation angle).


Torque-angle relation - increment ratio of torque-angle
It can be seen from the tightening process in the assembly process that when the bolt contacts from the beginning of screwing to the joint surface, the screwing torque is almost 0 or small as long as the thread accuracy is qualified and there is no bump. Then it enters the fitting stage, which begins to overcome some manufacturing errors and the roughness of the contact surface, as well as the elastic and plastic deformation of the clamped part. The relation between torque rise and Angle change in this section is nonlinear, and the torque value rises very fast. Then enter the stage of approximate elastic deformation, at this time torque and Angle is a linear relationship, the increase of Angle represents the increase of deformation, and is proportional to the change of preload force. When the preload reaches the yield point of the bolt, the bolt begins to enter plastic deformation. At this time, as long as the torque increment is small, the bolt will have a large extension, so that the Angle increment becomes large. So the ratio of increment of torque to increment of angle is greatly reduced, which indicates that the yield point is reached.