### Transcription of points: T=KxDxF T=FxX factor X K - Archetype Joint …

1 Measuring torque when installing controlled tensioning of a threaded fas- Authored by: *. threaded fasteners is the best indicator of tener while monitoring both torque and future **Joint** performance, right? Actually, tension. At a specified torque or tension, David Archer :4, 2t1. President bolt tension is a better performance indi- the known values for 7, D, and F are in- ln **Archetype** Fasteners LLC ',, cator, but measuring torque is far easier serted into the short-form equation to per- Orion, Mich. ,41. to do. mit solving for K. Bolt tension is created when a bolt elon- Many engineers use a single value of K Edited by Jessica Shapiro ,: gates during tightening, producing the across a variety of threaded-fastener diam- *. clamp load that prevents movement be- eters and geometries. This approach is valid Key points: .4. t tween **Joint** members.

2 Such movement is to some extent, because an experimentally . The experimentally determined *ta4. arguably the most common cause of struc- determined nut **factor** is by definition inde- nut factot K. consolidates the /a tural **Joint** failures. The relationship be- pendent of fastener diameter. But to truly friction effects on threaded- t!: fastener systems. tween applied torque and the tension cre- understand the **factors** involved, it is help- ful to compare the short-form equation . A nut **factor** determined for one tt ated is described by the relationship: **T=KxDxF** with a torque-tension relationship derived fastener geometry is valid for , from engineering principles. fasteners of similar geometry but :al different diameters. x where T = torque, K = nut **factor** , some- Several of these equations are common, ia times called the friction **factor** , D = bolt especially in designs that are primarily used.

3 Testing **Joint** prototypes y,;. g diameter, and F = bolt tension generated in the Each produces similar results highlig hts fastener interactions during tightening. This expression is often and takes the general form: and points out design flaws. t;. L. called the short-form equation. Resources: **T=FxX** *. n ArchetypeJoint !LC, The nut **factor** where X represents a series of terms w w w. a r ch ety pej o i nt. co m a, The nut **factor** , K consolidates all fac- detailing fastener geometry and friction ' **Joint** Decisions," Mncurnr Drsrcru, ar'. tat tors that affect clamp load, many of which coefficients. These relationships are often April 1, 2005, http://ti ,.7. *. are difficult to quantify without mechani- referred to as long-form equations. (Three "How Tight is Right?" Mncurr're ta cal testing. The nut **factor** is, in reality, a of the most widely used long-form equa- Drsren, August 23, 2001, ta:l ta, fudge **factor** , not derived from engineering tions are discussed in the sidebar, The long principles, but arrived at experimentally to wary').

4 Make the short-form equation valid. To understand how the nut **factor** com- Various torque-tension tests call for pares to the terms in the long-form equa- 40 I IVACHINE AUGUST 20,2OO9. i tions, let's consider the so-called Motosh equation: 7,,= Frx l(Pl2t) + (y,x r,lcos p1 + (y,x r,)J. where 7, = input torque, Fp = fastener pre- load, P = thread pitch, U,= friction coefficient in the threads, rr = effective radius ofthread contact, p = halfangle ofthe thread form (30'. for UN and ISO threads), l, = friction coef- ficientunderthenutorhead, andr =. effective radius ofhead contact. The equation is essentially three - terms, each of which represents a reaction torque. The three reaction torques must sum to equal the input torque. These elements, both dimen- sional and frictional, contribute in varying degrees to determining the torque-tension relationship, the pur- pose ofcalculating nut **factor** .)

5 The impact of variables So how do design decisions influ- ence the nut **factor** that defines the torque-tension relationship? Specifi- cally, engineers maywonder howvalid a nut **factor** determined from a torque- tension test on one twe of fastener is for other fastener geometries. The short-form equation is structured so that the fas- tests on one fastener diameter can be used to calculate the tener diameter, D, is separate from the nut **factor** , K. This torque-tension relationship for fasteners with a different implies that a nut **factor** derived from torque-tension diameter. AUGUST 20,2OO9 MACHINE I 41. r- ,,v I. FASTENING & JOINING. J. Like the nut Validating variables **factor** itself, how- 35o/o ever, this approach While the nut isonlyanipproxi- **factor** K, in mation. The ac- $J roo" the short-form equation is curacv of usine u F- experimentally F )\o/^.

6 Nomlnal lastener determined, diameter, D, to .g long-form applyaconstant !2aon equations use nut **factor** across E several variables a range of fastener 3 rcon to quantify sizes depends E the effects of on the extent to P thread pitch and " c ^^", lv-/o friction on the wnrcn lastener clr- ; torque-tension ameter affects re- .0. traces shown here help explain the effect each 4oo/o 600/o 80o/o 1$0o/o variable has on lncrease in variable (o/o) bolt tension. sense to examine them individually. importance of thread pitch falls. Clearance-hole diameter, for instance, is directly tied There is a maximum deviation of between the to nominal diameter. The long-form equations calculate results ofthe short and long-form equations for stan- that swapping a close-diametrical-clearance hole with dard-pitch, metric, hex-head-cap screws with constant one 10% larger leads to a 2o/o reduction in bolt tension and equal coefficients offriction.

7 As friction coefficients for a given torque. Enlarging the fastener-head bearing increase, there's less error in assuming the nut **factor** var- diameter by 35o/o, say by replacing a standard hex-head ies directly with nominal diameter because the impact of fastener with a hex-flange-head, cuts bolt tension by 8% thread pitch, the most independent variable, falls. for a given torque. So, if all else is held constant, it's reasonabie to apply Both bearing diameter and hole clearance generally a nut **factor** calculated at one fastener diameter across a scale linearly with bolt diameter, so their relative impor- range offastener sizes. For best resuits, engineers should tance remains the same over a range of fastener diame- base testing on the weighted mean diameter of the fasten- ters. However, different head styles or clearances change the reaction torque from underhead friction because the contact radius changes.

8 Doubling the thread friction coef- ficient on its own, say by changing the finish or removing lubricant, reduces 50. bolt tension by 28Vo for a given torque. Engineers should note that the thread 240. and underhead friction coefficients are CJ. often assumed to be equai for conve- x5u nience in test setups and calculations. ISO 16047 estimates that this assumD- 20. tion can lead to errors of I to 2o/o. Thread pitch tends to be more 10. indeoendent of nominal diameter thanlhe other variables. Increasing just thread pitch by 40% cuts tension 0l020304050. 5o/o for a given torque. However, the Tension (kN). reaction-torque term containing the thread pitch, P Torque-tension tests on simplified representative joints let engineers - Pl2n - does not contain a friction coefficient. There- determine a nut **factor** that can define the torque-tension relationship for similar fasteners with different diameters.

9 However, sample-to-sample fore, as fastener diameter and, conse- variations in friction can make results vary by as much as 10o/o. quently, friction increase, the relative 42 MACHINE AUGUST 20, 2009. a; .f the long- The long and short of it ri)r:m equa- Theshort-form tlons get en- equation, I=K. xDxF,usingan gli'eers closer experimentilly to the "right". derived nutfactor, aF 'wer thanks F= ,K= K,givesslightly to their fun- f=008,K=0115 different results cor- 90ok -i '-i thanthelong-form re tness. How- >s;: -:l equationovera e,. - r lnno_fnrm ""'. xii rangeoffastener "'""b Q B0olo -r-, sizesasshown here ei atlons' even xl v fortwo different \'! en oerlveo frictionlevels. tI. n enqlneer- 700/0 ;--'-.*- Results fall within ing principles, i: I. 5oloofeachother. u, l assumP- l Thevaluesforpand ti ns and ap- 600/0! :- :, - "M.

10 -,;.. , ,..,-,,..,.."-,..,., ,..:,.- .. ,. ,-,; ," ';-) Kwere chosen to pr ximations -. -- - - M5 M6 Mlo M12 M14 M16 M20 M22 M24 normalizetracesfor ih t may make Ml2fasteners. tt m no more Nominal fastener diameter , ,:i,r,t:t,t,t1: I t,t: I i :.. :-.:::':' :' '.. (lC fect than an rr( ation using ers forwhich the nut **factor** will be used. an experimentally derived nut **factor** . Many engineers find it expedient to apply a single nut The potential errors in both types of e uations pale **factor** across even greater fastener ranges, such as those compared to the variations in real-world jo, ts. Benchtop with different head styles or clearance diameters. Apply- torque-tension testing shows approximate y 10% varia- ing the nut **factor** to joints where geometric variables other tions within samples even when all fastt:ner and bearing than nominal diameters are changing causes the short- materials are the same.)