Technology >>扣件博士Q&A：
重新探究扭矩法

Q&A with Dr. Fastener
Reviewing the TorqueControl Method
Tell me how to determine the value of
Q1: tighteningtorque.

A:The value of tightening torque changes with the target axial bolt force andthe nominal diameter of the threads. Specifically, we can calculate thetightening torque required for fastening by multiplying the product of axial
force and nominal diameter by a coefficient called “nut factor”. This expression is
the simplified form of an exact equation derived from the balances of the forces andtorques on the thread surface and nut bearing surface. The most commonly-used
numeric value for the nut factor is 0.2. This value corresponds to a standard value ofcoefficient of friction, i.e., 0.15, but note that the nut factor greatly changes according
to coefficient of friction.

Q2:

Hardware & Fastener Components - no.56/2022

A:

062

I don’t understand what a nut factor means.
How does it affect fastening operation?

The mechanically exact expression, which shows the relationship between
axial bolt force and tightening torque, contains the term pertaining tothe friction on the thread surface and nut bearing surface, in addition to the term
pertaining to the axial force generated when the male thread climbs up the inclined
surface. This is a complex expression involving trigonometric functions, and therefore
we usually use the simplified expression (Tightening torque = nut factor x axial force
x thread nominal diameter). Consequently, nut factor can be regarded as a coefficientfor calculating tightening torque for a given axial bolt force and the size of threads tobe used. The value of nut factor K changes because of several reasons, but practicallyspeaking, we can calculate it as the functions of thread surface's COF, μth, and nut
bearing surface's COF, μ nu. This expression is derived by applying a statistical method
called least squares method to the exact expression showing the relationship between
axial force and torque. The constants in the expression represent the components bywhich the torque is converted to axial force. It suggests, therefore, that most of thetightening torque is consumed as friction works.

the purpose of inspection, I fastened
Q3: Forthe loosened threads again using the sameamount of torque in the initial tightening
operation, but it turned out the obtained axial
force is insufficient. Why is that?

A:

This is because “even if you apply the same tightening torque, the valueof axial force changes with coefficient of friction”. As shown in the above
expression, the nut factor is expressed as the function of coefficient offriction. Using the expression andsupposing that the coefficients offriction of the thread surface and nut
bearing surface are both 0.15 and 0.3,
the amounts of nut factor are found tobe 0.2 and 0.381. Consequently, whena bolted joint's coefficient of frictionchanges from 0.15 to 0.3 because of
the increase of the surface roughness
due to tightening a nd loosening,
only 52% of the target axial force isgenerated even if you apply the sametorque. We can also say that “evenif we apply the same torque, theaxial force to be generated is almost
inversely proportional to coefficientof friction.” This is a noteworthy phenomenon
in a bolted joint which is repeatedly fastened
and loosened. Contrary to the above case, thecoefficient of friction could become smaller
than the initial value. In that case, we must
pay attention to plastic deformation due to theexcessive axial force.

feel the loosening
Q4: Itorqueis smaller than
the tightening torque.
Is that so?

A:T h a t i s r ig h t . W h e n fa s t e n i n gthreads, the male threads move up
the thread surface along the helix,
thereby generating axial force. The lead angle,
which is the spiral angle of thread surface,
is usually from 2 to 3 degrees. On the otherhand, the male threads move down along thethread surface when being loosened; therefore,
the loosening torque is usually smaller than
the tightening torque. The ratio of the twotorques can be calculated using an expression
derived mechanically. For instance, when
the coefficient of friction ranges from 0.1 toaround 0.2, we can loosen the threads witha torque which is from 70% to 80% of thetightening torque. The ratio of the two torques
decreases with smaller coefficient of friction
and smaller nominal diameter. In contrast, theratio gets quite large in fine threads. If you feelthe loosening torque is too large, you should
suspect the occurrence of “seizure of threadedfasteners”.

Reference
1. Toshimichi Fukuoka, "Threaded Fasteners
for Engineers and Design – Solid Mechanics
and Numerical Analysis –", pp.76-100,
Corona Publishing Co., Ltd. (2015)

Article by Toshimichi Fukuoka
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