Effect of friction coefficient on axial clamping force of threaded fasteners

The threaded connection is to use the threaded fasteners to reliably connect the connected parts together, essentially controlling the axial clamping force, and is subject to structural function, part strength, process control method and control precision, and friction of the connecting pair during assembly. The impact of many factors such as performance. The tightening of the bolt fasteners is a process that overcomes the friction between the support surface and the friction between the threads. 90% of the total energy is used to overcome the friction, and only about 10% of the capacity is used to provide the axial clamping force.

The friction coefficient of threaded fasteners is affected by many factors such as material, surface treatment, manufacturing process and thread precision. The relationship between total friction coefficient μ and tightening torque T and axial clamping force F is as shown in equation (1). Shown as follows:

(1)

In the formula, P is the pitch, d2 is the middle of the thread, and Db is the friction diameter of the lower support surface of the bolt head. The clamping force F can be expressed by the formula (2):

(2)

When the test bolt is selected, d2 and Db are fixed. When the tightening torque T is constant, the larger the total friction coefficient, the smaller the axial clamping force F acting on the thread.

Theoretically, the relationship between the tightening torque T during bolt tightening, the axial clamping force F of the bolt and the friction coefficient and the size of the thread shape is as shown in equation (3):

(3)

Where, ms is the coefficient of friction of the thread pair; mw is the coefficient of friction of the end face; dp is the effective diameter of the bolt, the coarse thread dp»0.906d; dw is the equivalent diameter of the end face friction circle,

Du and di are respectively the outer diameter and inner diameter of the friction circle; d is the nominal diameter of the thread; b is the angle of the thread, and a is the half angle of the thread in the vertical section, which is about 29°58¢. The first, second, and third terms on the right side of (3) can be understood as the torque consumed by the thread pair friction, the torque consumed by the bolt extension (the axial clamping force), and the torque consumed by the end face friction.

When the bolt is tightened, it is subjected to the tensile-torsional composite stress. According to the third strength theory, the bolt allowable equivalent stress σv can be obtained according to the formula (4).

(4)

Where σ is the tensile stress generated by the axial clamping force F of the bolt,

Ï„ is the shear stress generated by the torque Ts of the bolt portion,

According to the formula 3, the torque on the bolt is applied:

And take tgβ=0.05 (coarse thread), dp=1.05ds substitute (4) can be obtained:

(5)

It can be seen from equation (5) that the larger the friction coefficient of the thread pair, the greater the equivalent stress of the bolt under the same axial force. In other words, after the bolt strength is selected, the larger the friction coefficient, the smaller the axial force that the bolt can withstand, and the smaller the friction coefficient, the greater the axial force that the bolt can withstand.

The friction coefficient is a comprehensive index for evaluating the bolt manufacturing level. The magnitude of the friction coefficient determines the torque value and the axial clamping force. The dispersion of the friction coefficient affects the axial clamping force that the bolt can provide during assembly . In particular, when the bolt is tightened by the torque method, the difference in the friction coefficient is larger. In order to ensure the axial force of the assembly, the range of the assembly torque must be strictly controlled, and the assembly tool with higher precision must be used, resulting in an increase in assembly cost.

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