Measuring torque when installingthreaded fasteners is the best indicator offuture joint performance, right? Actually,bolt tension is a better performance indi-cator, but measuring torque is far easierto do.

Bolt tension is created when a bolt elon-gates during tightening, producing theclamp load that prevents movement be-tween joint members. Such movement isarguably the most common cause of struc-tural joint failures. The relationship be-tween applied torque and the tension cre-ated is described by the relationship:

T=KxDxFwhere T = torque, K = nut factor, some-times called the friction factor, D = boltdiameter, and F = bolt tension generatedduring tightening. This expression is oftencalled the short-form equation.

The nut factorThe nut factor, K consolidates all fac-

tors that affect clamp load, many of whichare difficult to quantify without mechani-cal testing. The nut factor is, in reality, a

fudge factor, not derived from engineeringprinciples, but arrived at experimentally tomake the short-form equation valid.

Various torque-tension tests call for

controlled tensioning of a threaded fas-tener while monitoring both torque andtension. At a specified torque or tension,the known values for 7, D, and F are in-serted into the short-form equation to per-mit solving for K.

Many engineers use a single value of Kacross a variety of threaded-fastener diam-eters and geometries. This approach is validto some extent, because an experimentallydetermined nut factor is by definition inde-pendent of fastener diameter. But to trulyunderstand the factors involved, it is help-ful to compare the short-form equationwith a torque-tension relationship derivedfrom engineering principles.

Several of these equations are common,especially in designs that are primarily usedin the E.U. Each produces similar resultsand takes the general form:

T=FxXwhere X represents a series of termsdetailing fastener geometry and frictioncoefficients. These relationships are oftenreferred to as long-form equations. (Threeof the most widely used long-form equa-tions are discussed in the sidebar, The longwary')

To understand how the nut factor com-pares to the terms in the long-form equa-

Authored by:

David ArcherPresidentArchetype Fasteners LLC

Orion, Mich.

Edited by Jessica Shapirojessica.shapi ro@penton.com

Key points:. The experimentally determinednut factot K. consolidates thefriction effects on threaded-fastener systems.

. A nut factor determined for onefastener geometry is valid forfasteners of similar geometry butdifferent diameters.

.Testing joint prototypeshighlig hts fastener interactionsand points out design flaws.

Resources:ArchetypeJoint !LC,w w w. a r ch ety pej o i nt. co m

'Joint Decisions," Mncurnr Drsrcru,

April 1, 2005, http://ti ny.cc/ZgcTy

"How Tight is Right?" Mncurr're

Drsren, August 23, 2001,http://tiny.cc/tH8zc

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tions, let's consider the so-called Motoshequation:7,,= Frx l(Pl2t) + (y,x r,lcos p1 + (y,x r,)Jwhere 7, = input torque, Fp = fastener pre-load, P = thread pitch, U,= friction coefficientin the threads, rr = effective radius ofthreadcontact, p = halfangle ofthe thread form (30'for UN and ISO threads), l, = friction coef-ficientunderthenutorhead, andr =

-effective radius ofhead contact.

The equation is essentially threeterms, each of which represents a

reaction torque. The three reactiontorques must sum to equal the inputtorque. These elements, both dimen-sional and frictional, contribute invarying degrees to determining thetorque-tension relationship, the pur-pose ofcalculating nut factor.

The impact of variablesSo how do design decisions influ-

ence the nut factor that defines thetorque-tension relationship? Specifi-cally, engineers maywonder howvalida nut factor determined from a torque-tension test on one twe of fastener isfor other fastener geometries.

The short-form equation is structured so that the fas-tener diameter, D, is separate from the nut factor, K. Thisimplies that a nut factor derived from torque-tension

tests on one fastener diameter can be used to calculate thetorque-tension relationship for fasteners with a differentdiameter.

MACHINE Design.com I 41AUGUST 20,2OO9

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Like the nutfactor itself, how- 35o/o

ever, this approachisonlyanipproxi- $ roo"mation. The ac- Jcuracv of usine u F-F )\o/^nomlnal lastenerdiameter, D, to .gapplyaconstant !2aonnut factor across Ea range of fastener 3 rconsizes depends Eon the extent to P

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While the nutfactor K, inthe short-formequation isexperimentallydetermined,long-formequations useseveral variablesto quantifythe effects ofthread pitch andfriction on thetorque-tensionrelationship.Thetraces shownhere help explainthe effect eachvariable has onbolt tension.

sense to examine them individually.Clearance-hole diameter, for instance, is directly tied

to nominal diameter. The long-form equations calculatethat swapping a close-diametrical-clearance hole withone 10% larger leads to a 2o/o reduction in bolt tensionfor a given torque. Enlarging the fastener-head bearingdiameter by 35o/o, say by replacing a standard hex-headfastener with a hex-flange-head, cuts bolt tension by 8%for a given torque.

Both bearing diameter and hole clearance generallyscale linearly with bolt diameter, so their relative impor-tance remains the same over a range of fastener diame-ters. However, different head styles orclearances change the reaction torquefrom underhead friction because thecontact radius changes.

Doubling the thread friction coef-ficient on its own, say by changing thefinish or removing lubricant, reducesbolt tension by 28Vo for a given torque.Engineers should note that the threadand underhead friction coefficients areoften assumed to be equai for conve-nience in test setups and calculations.ISO 16047 estimates that this assumD-tion can lead to errors of I to 2o/o.

Thread pitch tends to be moreindeoendent of nominal diameterthanlhe other variables. Increasingjust thread pitch by 40% cuts tension5o/o for a given torque. However, thereaction-torque term containing thethread pitch, P - Pl2n - does notcontain a friction coefficient. There-fore, as fastener diameter and, conse-quently, friction increase, the relative

importance of thread pitch falls.There is a maximum deviation of 4.2o/o between the

results ofthe short and long-form equations for stan-dard-pitch, metric, hex-head-cap screws with constantand equal coefficients offriction. As friction coefficientsincrease, there's less error in assuming the nut factor var-ies directly with nominal diameter because the impact ofthread pitch, the most independent variable, falls.

So, if all else is held constant, it's reasonabie to applya nut factor calculated at one fastener diameter across a

range offastener sizes. For best resuits, engineers shouldbase testing on the weighted mean diameter of the fasten-

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Torque-tension tests on simplified representative joints let engineersdetermine a nut factor that can define the torque-tension relationship forsimilar fasteners with different diameters. However, sample-to-samplevariations in friction can make results vary by as much as 10o/o.

42 MACHINE Design.com AUGUST 20, 2009

The long and short of it

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Theshort-form ri)r:m equa-equation, I=K tlons get en-xDxF,usingan gli'eers closerexperimentilly to the "right"derived nutfactor, aF 'wer thanksK,givesslightly to their fun-different results da.nental cor-thanthelong-form re tness. How-equationovera e,. r lnno_fnrmrangeoffastener - "'""b ""'sizesasshown here ei atlons' even

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ers for which the nut factor will be used.Many engineers find it expedient to apply a single nut

factor across even greater fastener ranges, such as thosewith different head styles or clearance diameters. Apply-ing the nut factor to joints where geometric variables otherthan nominal diameters are changing causes the short-form-equation results to differ from the long-form resultsbyupto l5%.

Long or short?So given all the discussion about which variables im-

pact the nut factor and when it is reasonable to use a con-stant nut factor across a range offasteners, it may seem

an experimentally derived nut factor.The potential errors in both types of e uations pale

compared to the variations in real-world jo, ts. Benchtoptorque-tension testing shows approximate y 10% varia-tions within samples even when all fastt:ner and bearingmaterials are the same. According to both s, trt and long-form equations, there should be no variatir n at all. Fric-tion coefficients seem to vary from sample t sample.

The situation is even worse in prodtr.ct )n-represen-tative joints. One in-joint torque-lension est with bolttension measured in real time using ultraso c pulse-echotechniques revealed variations inherent in how compo-nents fit together. A slx-bolt pattern magnil ed the effects

of imperfect contacl i :tween boltsand the bearing surfa ce ind produceda 607o sample-to-sample variationbecause both geometric and frictionvariables were changinS tver the sam-ple set.

The bottom line is t it neither thenut factor nor the lon -form equa-tion's friction coefficier .s can be reli-ably established using reference ta-bles. Only testing acci,rately deter-mines friction conditicns. As we haveseen, these are too sensitive to com-ponent and assembly variation to bedetermined by analysis lone.

Testing reliably c verts inputtorque to induced te ion, Iettingengineers determine ean frictioncoefficients or nut fa iors and thedistributions about 1 rose means.Tests may also help en;ineers iden-tify inherent shortcomings in jointsthat need to be revised o make themmore reliable. MD

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Torque-tension tests on prototype joints, like this one on a six-bolt pattern,can highlight design problems in joint design. ln this <ase, variations of up to600lo from sample to sample indicated that the joint geometry was magnifyingthe effects of imperfect contact between fastener and bearing surface.

AUGUST20,2009 IVACHINEDesign,com