by Christopher Bunai - SmartBolts

1 As a result of this trend, a common ques-tion from many engineers, mechanics , main-tenance personnel and assemblers is: Howmuch torque do I need to install this fasten-er? The best, but perhaps not very helpful,answer is: Whatever amount of torque isneeded to develop the proper tension. The problem with this response is thatunder most circumstances, the ability tomeasure tension is not available. What hastraditionally been available, however, aretorque wrenches, and thus the ability tomeasure to answer this question leadsus to the torque-tension relationship and abrief explanation of how torque and tensionrelate. Torque is the rotational forceused toturn the nut or fastener head in a boltedjoint.

2 As torque is applied to the nut, itattempts to climb up the threads of the boltreducing the grip length; however, when thecomponents within the grip resist, the boltis forced to stretch. As the bolt elongates, itbehaves like a spring and develops tension,also known as preload. The tension devel-oped within the bolt has an equal and oppo-site reaction1on the bolted components,which creates the all-important clamp force,the compressive force holding the boltedjoint members installing a bolt, a common prac-tice is to find a torque table and look up thetorque value listed by size, thread, grade,plating, presence or absence of lubrication,and other various properties of the boltbeing used.

3 An abbreviated torque tableexample is shown in Figure 1. As an exam-ple, we will use a 1/2 -13 SAE Grade 5 ZincDichromate bolt. For our bolt sample, thistable recommends an installation torque of75 ft. lbs. Where does this value come from?The torque value is actually a calculatedquantity from the short form torque-preloadequation. Bickford (1995) states the equa-tion as, T = K F D,where T, K, F, and D arethe input torque, the nut factor, theachieved preload, and bolt s nominal diame-ter, respectively (Bickford, 1995, p. 226).The nut factor is an empirical value thatlinearly models the rate at which tension isdeveloped within a fastener when torque isapplied.

4 The nut factor convenientlydescribes all of the many variables that areknown to influence the torque-tension rela-tionship. Properties affecting this relation-ship include: the material and size of thebolt, nut and washer, type of plating, surfacefinish, corrosion and wear on threads, pres-ence and type of thread lubricant, and thenumber of times the bolt has been previous-ly fastened, to just name a a more in-depth look at the use ofthe short form torque preload equation, awell presented discussion can be found inthe article Dissecting the Nut Factor writ-ten by Dave , the desired preload should beknown and based on the bolted jointrequirements as well as bolt strength limita-tions.

5 As a note, many torque charts like theone shown earlier use a standard value of 75percent of the bolt s proof load. The desiredpreload can then be used within this equa-tion along with the experimentally deter-mined nut factor. In our example, a 1/2 -13 SAE Grade 5 bolt has a proof load of approx-imately 12,000 lbs., and 75 percent of this is9,000 lbs. Clearly, the bolt s nominal diame-ter is the easiest piece of information todetermine and is conveniently specified ininches for this case first. The product ofthese variables result in an input torquevalue with units of in. lbs., although theequation can be divided by 12 to convert toft. lbs.

6 As can be seen from the equationbelow, we are able to produce the value ofMost fasteners are tightened using traditional methods, such as manual torque wrenching, pneumatic impact wrenching, or automatic torque cutoff Christopher BunaiThe Torque-TensionRelationship GetsSTRETCHED1 Usually, but not always. See p. 182 of Bickford formore information on the 1. Abbreviated Torque Chart ExampleThe torque calculations in this chart are provided as a guide only. Due to the many factors that affectthe torque-tension relationship, such as material, surface finish, lubrication, etc., the torque-tensionrelationship should be established experimentally. Use at your own Grade 5 Torque Values in ft.

7 = = = inch7/16 143750621/2 135675949/16 1282109136 Reprinted from American Fastener JournalMay/June 201275 ft. lbs. shown in the provided where is the problem? The quickanswer is the nut factor, K, can vary. Onething you may notice about any publishedtorque chart is a disclaimer that readssomething like The torque calculations in thischart are provided as a guide only. Due to the manyfactors that affect the torque- tension relationship,such as material, surface finish, lubrication, etc., thetorque- tension relationship should be establishedexperimentally. Use at your own risk. This dis-claimer is there for a reason: The nut factornot only varies between sizes, materials andfinishes; it can vary between identicallyspecified bolts.

8 It can even vary for the samebolt!The nut factor utilized, either from thecharts or experimentally developed, shouldbe based on a statistical sample. The sam-ple mean and standard deviation can thenbe calculated. Using the mean and threestandard deviations justifies the likelihoodthat the nut factor can easily vary betweenthe values shown in the graph. This range <K< applies for normal does not include the factors that coulddrastically change the torque-tension rela-tionship, such as poor or damaged threadgeometry, the use of a lubricant withoutknowing its effect on the nut factor, or irreg-ular embedment of the underside face of thebolt into a soft washer, etc.

9 If any of theseconditions occur, the nut factor could rangeas high as or as low as The effect ofthe dramatic nut factor variation is shown bythe Over Lubricated and Excessive Fric-tion lines in Figure 2. It can be seen thatusing the recommended value of 75 ft. the over-lubricated bolt would cause theyield strength of the bolt to be exceeded. Inthe case of the bolt experiencing excessivefriction, the developed preload would beapproximately 3,500 lbs., only 38 percent ofthe desired that the installer is intention-ally keeping torque relatively constant dur-ing installation, and it can be seen that thevitally important fastener tension varieswhen the nut factor varies!

10 Other than thepotentially misleading click of a torquewrench, the bolt installer has little to nofeedback that tension has been under, over,or properly developed. To be fair, fracture ofthe bolt would be noticeable feedback if theultimate tensile strength were exceeded inthe under-lubricated case or the ultimateshear strength were exceeded in the exces-sive friction back to Figure 2, the yellowarea represents a standard torque wrenchwith an accuracy of +/-3 percent that canonly reliably tighten a group of bolts to +/-30 percent of desired tension (Bickford,1995, p. 222). At this point, it is worth notingthat a more accurate torque wrench doesnot improve this discrepancy red box is shown with a very narrowband on the installation torque axis, imply-ing accurate installation torque , it also shows large variation in thedeveloped tension axis under irregular, butplausible and potentially catastrophic, what is the solution?