“Coefficient of Friction” vs. “Nut Factor”

Published by LGG Industrial

Both of the terms “Coefficient of Friction” and “Nut Factor” are frequently used when speaking about gaskets – in particular, about the squeezing of gaskets between flanges.  This is because the compression of the gasket is most often accomplished by the application of stud load that is generated by torquing a nut.  So [1] turning a nut [2] stretches the stud, which is creates a [3] compressive load on the gasket.   


Long-term gasket sealability is completely dependent on gasket stress, and the best sealing programs target very specific gasket stresses.  But In order to be able to know if the gasket is actually being loaded to the specified target, we must be able to define the relationship between the force applied in turning the nut and the amount of stress generated in the stud.


Coefficient of Friction

When sliding one surface over another, the amount of force required is dependent on the frictional drag.  Sliding a block of ice over a steel plate requires a lot less force than a bale of hay weighing the same amount.  The ratio between the force required to move an object over another surface and the pressure between those surfaces is called the Coefficient of Friction.  Since ice is far more slippery than hay, the Coefficient of Friction is much lower. 


The use of an anti-seize product in bolted connections makes it easier to move one metal surface over another.  The manufactures of these products experimentally determine the Coefficient of Friction imparted by that product when used between specific fastener materials.  That Coefficient of Friction is often reported on the can, or in the technical bulletins for that product.   


In the simple action of turning a nut onto a stud, a number of interactions take place which involve the Coefficient of Friction.  The point of highest “drag” is where the nut surface turns against the stationary flange surface.  Obviously, as the load on the stud increases, the pressure at this nut/flange interface increases, requiring more force to slide the one surface on the other.  This force requirement is defined by the Coefficient of Friction.


Likewise, the stud and the nut both have thread surfaces that are sliding against each other.  These threads are simply coiled slopes, which can be visualized as two inclined planes that are slid past each other.  The Coefficient of Friction defines the amount of force required to move those planes relative to each other, but the equations that describe this interaction must take into account the pitch diameter of the threads and the helical angle of the sloped planes perpendicular to the axis of the stud.


The total torque required to achieve the needed stud stress is a sum of the torque required due to the nut/flange interface, and the torque required due to the thread interactions.  And while very accurate torque values can be computed using this detailed approach, it does require a fairly complex set of equations to do so.  Fortunately, there is a much simpler approach that gives very reliable results. 


The Nut Factor

The Nut Factor (K) combines the thread geometry, the pitch, the friction at the nut face and the friction on the threads into one overall value.  This allows us to write a very simple equation to describe the relationship between the torque on the nut and the load developed by the stud.  That equation is:

Torque ( = Load (pounds) x Nominal Stud Size (inches) x Nut Factor / 12

While less comprehensive than equations built around the use of the Coefficient of Friction, this equation yields very good results for the standard fasteners used in the process industries. 


So the torque required to generate 50,000 pounds of load on a 1-1/8” stud, using an anti-seize with a nut factor of 0.17 would be:

Torque ( = 50,000 (pounds) x 1.125 (inches) x 0.17 / 12 = 797

The Nut Factor (which has no units) is experimentally determined by the anti-seize manufacturer, and usually falls between 0.15 and 0.20. 


Comparing the Coefficient of Friction to the Nut Factor

Both the Coefficient of Friction and the Nut Factor speak to the frictional drag in a bolted connection.  However, they are not the same thing, and the terms cannot be used interchangeably.  Unfortunately, these terms are often confused, and the values are used in the wrong equations, giving inaccurate results. 


Both the Coefficient of Friction and the Nut Factor are determined by the manufacturer, and the end-user must make sure he understands which value is being reported. 

As a general rule, the Coefficient of Friction is on the order of 0.04 LESS THAN the Nut Factor, and runs between 0.11 and 0.16. 



ERIKS uses the Nut Factor to convert torque to stress in all of our computational worksheets, including the Exchanger Gasket Workbook.