# Efficient Plant April 2018 - 12

```feature | mro solutions

Torque
coefficient
for 1- to
12-thread
bolt

0.7

µ = coefficient of friction of bolt and material in the

0.6

threaded area
µc = coefficient of friction between the bolt collar and
the material
α = radial angle of the thread
λ = thread lead angle

0.5
0.4
0.3
0.2
0.1
0

0.1

0.2

0.3

0.4.

0.5

Coefficient of friction in threads and collar

0.6

Fig. 1. Coefficient of friction 'µ' vs. torque coefficient 'K'

The whole
point of the
design is
obtaining
the correct
clamping
force.

is readily measured with a calibrated torque wrench.
For reasons that will be explained later, the error associated with this method, however, can be as high as
+/-30%. (That's why, in some structural applications,
torque tables are not allowed.)
While the torque measurement itself is relatively
easy to accomplish with good accuracy, the actual
clamping force resulting from the tightening torque
can be significantly higher or lower than the desired
clamping force. Of course, the whole point of the
design is to obtain the correct clamping force.
Equation 1 is commonly used to determine how
much torque is needed to accomplish a certain clamping force in a bolted joint. Observe that there are two
main components in the equation (see italicized text
underneath the equation):
 the amount of torque needed to overcome friction
between the engaged threads as the bolt is stretched
 the amount of torque needed to overcome friction
between the bolt collar and the mating surface under
the bolt collar.
Equation 1:
T = F [(dp/2)(µ + tanλ cosα) / (cosα - µ tanλ)] + F(dc/2)µc
friction of
engaged threads

Where:
T = applied tightening torque
F = clamping force
dp = pitch diameter of bolt

12

| EFFICIENTPLANTMAG.COM

bolt-collar
friction

Of all the factors in Equation 1 that are needed
to determine the necessary tightening torque, only
two are actually variable: the overall coefficient of
friction between the engaged threads and the overall
coefficient of friction between the bolt collar and the
material surface.
The other factors in Equation 1, such as thread
pitch diameter, thread lead angle, collar diameter, and
thread radial angle, are automatically determined by
the choice of bolt.
In most cases for UNC and UNF bolts, for example,
the value for the radial angle α is 30 deg., so
cos 30 deg. is 0.866. If, say, there are 12 threads/in.
on a bolt, then tan λ is 1/12 or 0.0833. Likewise, if
there are 8 threads/in., tan λ is 0.125, and so on. With
this information in mind, we can see that, when
otherwise identical bolts are compared to each other,
Equation 1 can be simplified as Equation 2 below (if
there are 12 threads/in. and the radial angle is 30 deg.)
Equation 2:
T = KFd

Where:

torque

K = (0.5m + 0.036)/(0.866 - 0.0833µ) + 0.625µc = coefficient

d = nominal bolt diameter
F = clamping force
T = applied torque

Equations 1 and 2 show the importance of the
bolt-collar component. It's not unusual for, perhaps,
40% of the required tightening torque to be due to
the friction between the bolt collar and the bolted
material, and 60% due to the friction between the
engaged threads.
For a bolt with 12 threads/in. and a radial angle
of 30 deg., Fig. 1 shows a plot of the coefficient of
friction µ versus the resulting torque coefficient K.
The plot assumes that the engaged threads and the
bolt-collar contact area have the same coefficient of

APRIL 2018

```
http://www.EFFICIENTPLANTMAG.COM

# Table of Contents for the Digital Edition of Efficient Plant April 2018

Editorial
Implementations
What's Wrong With My Bolts?
Understand Vertical Motor Bearings
Bourbon Boom Drives Distillery Expansion
Lubricant Myths That Can Cost You
IIoT
SAP: When To Update SAP Master Data
Give Your Chain A 'Hand'
Why Do Hackers Hack?
Why Compressor Size Matters
Equipment-Rental Considerations
On The Floor
Microgrids Are On The Rise
Solution Focus
Products
Index
Showcase
Seeking Reliability
Efficient Plant April 2018 - Cover1
Efficient Plant April 2018 - Cover2
Efficient Plant April 2018 - 1
Efficient Plant April 2018 - 2
Efficient Plant April 2018 - 3
Efficient Plant April 2018 - 4
Efficient Plant April 2018 - 5
Efficient Plant April 2018 - Editorial
Efficient Plant April 2018 - 7
Efficient Plant April 2018 - Implementations
Efficient Plant April 2018 - 9
Efficient Plant April 2018 - What's Wrong With My Bolts?
Efficient Plant April 2018 - 11
Efficient Plant April 2018 - 12
Efficient Plant April 2018 - 13
Efficient Plant April 2018 - 14
Efficient Plant April 2018 - 15
Efficient Plant April 2018 - Understand Vertical Motor Bearings
Efficient Plant April 2018 - 19
Efficient Plant April 2018 - 20
Efficient Plant April 2018 - Bourbon Boom Drives Distillery Expansion
Efficient Plant April 2018 - 22
Efficient Plant April 2018 - 17
Efficient Plant April 2018 - 18
Efficient Plant April 2018 - 19
Efficient Plant April 2018 - 20
Efficient Plant April 2018 - Bourbon Boom Drives Distillery Expansion
Efficient Plant April 2018 - 22
Efficient Plant April 2018 - 23
Efficient Plant April 2018 - 24
Efficient Plant April 2018 - Lubricant Myths That Can Cost You
Efficient Plant April 2018 - 26
Efficient Plant April 2018 - 27
Efficient Plant April 2018 - 28
Efficient Plant April 2018 - IIoT
Efficient Plant April 2018 - SAP: When To Update SAP Master Data
Efficient Plant April 2018 - Give Your Chain A 'Hand'
Efficient Plant April 2018 - Why Do Hackers Hack?
Efficient Plant April 2018 - Why Compressor Size Matters
Efficient Plant April 2018 - Equipment-Rental Considerations
Efficient Plant April 2018 - On The Floor
Efficient Plant April 2018 - 36
Efficient Plant April 2018 - Solution Focus
Efficient Plant April 2018 - 38
Efficient Plant April 2018 - 39
Efficient Plant April 2018 - 40
Efficient Plant April 2018 - Products
Efficient Plant April 2018 - 42
Efficient Plant April 2018 - 43
Efficient Plant April 2018 - 44
Efficient Plant April 2018 - 45
Efficient Plant April 2018 - Index
Efficient Plant April 2018 - Showcase
Efficient Plant April 2018 - Seeking Reliability
Efficient Plant April 2018 - Cover3
Efficient Plant April 2018 - Cover4
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