Bolt Preload Calculation Procedur Procedure e Question: How is bolt installation preload calculated? Answer: Bolt pretension, also called preload or pre-stress, comes from the installation torque T
you apply when you install the bolt. The inclined plane of the bolt thread helix converts torque to bolt pretension. Bolt preload is computed as follows. i ! T"#$ %& #'q. (& where i ! bolt preload #called )i in *hi+ley&. T ! bolt installation torque. $ ! torque coefficient. % ! bolt nominal shan diameter #i.e., bolt nominal sie&. Torque coefficient $ is a function of thread +eometry, thread coefficient of friction µt, and collar coefficient of friction µc. oo up $ for your specific thread interface and collar #bolt head or nut annulu annulus& s& interf interface ace materi materials als,, surfac surfacee condit condition ion,, and lubric lubricant ant #if any&. any&. #/To #/Torqu rquee spe specs cs for screws,/ screws ,/ *hi+ley, and various other sources discuss various $ value estimates.& 0f you cannot find or obtain $ from credible references or sources for your specific interfaces, then you would need to research to try to find the coefficients of friction for your specific interfaces, then calculate $ yourself usin+ one of the followin+ two formulas listed below #*hi+ley, Mechanical Engineering Design, Design, 1 ed., 2c3raw-Hill, (454, p. 678, 'q. 5-(4, and 20-H%B$-89, (449, *ect. (99.1.(, p. 8, 8, 'q. (99.1.(, respectively&, the latter b ein+ far simpler. $ ! ;<#9.1 d p&#tan λ = µt sec β&"#( > µt tan λ sec β& = <9.81 µc %@"% #'q. & $ ! ;<9.1 p ;<9.1 p""π = <9.1 µt #% > 9.A1 p 9.A1 p sin sin α&"sin α = <9.81 µc %@"% #'q. 6& where % ! bolt nominal shan diameter. p ! p ! thread pitch #bolt lon+itudinal distance per thread&. 89 #for 2, 2C, DE, DEF, and DEC thread profiles&. α ! thread profile an+le ! 89 β ! thread profile half an+le ! 89" ! 69. tan λ ! thread helix an+le tan ! p ! p"# "#π d p&. d p ! bolt pitch diameter. µt ! thread coefficient of friction. µc ! collar coefficient of friction. % an a nd p can can be obtain obtained ed from bolt bolt tabl tables es such as *tandard 2etric and D*G Bolt *han %imensions.. %imensions The three terms in 'q. 6 are axial load component #coefficient& of torque resistance due to #(& thread thread helix helix incli inclined ned plane plane normal normal force, force, #& thread thread helix helix inclin inclined ed plane plane tan+ent tan+ential ial #threa #thread d friction& force, and #6& bolt head or nut washer face friction force, respectively.
However, whether you loo up $ in references or calculate it yourself, the en+ineer must understand that usin+ theoretical equations and typical values for $ and coefficients of friction merely +ives a preload estimate. oefficient of friction data in published tables vary widely, are often tenuous, and are often not specific to your specific interface combinations and lubricants. *uch thin+s as unacnowled+ed surface condition variations and ignored dirt in the internal thread can sew the results and produce a false indication of preload. The en+ineer and technician must understand that published $ values apply to perfectly clean interfaces and lubricants #if any&. 0f, for example, the threads of a steel, inc-plated, $ ! 9., /dry/ installation fastener were not clean, this mi+ht cause $ to increase to a value of 9.6 or even hi+her. Ine should also note that published $ values are intended to be used when applyin+ the torque to the nut. The $ values will chan+e in relation to fastener len+th and assembly runnin+ torque if the torque is bein+ read from the bolt head. Ine should measure the nut or assembly /runnin+/ torque with an accurate, small-scale torque wrench. #/Funnin+/ torque, also called prevailin+ torque, is defined as the torque when all threads are fully en+a+ed, fastener is in motion, and washer face has not yet made contact.& The only torque that +enerates bolt preload is the torque you apply above runnin+ torque. G few more thin+s to be aware of are as follows. Bolt proof stren+th * p is the maximum tensile stress the bolt material can withstand without encounterin+ permanent deformation. ublished bolt yield stren+ths are determined at room temperature. Heat will lower the yield stren+th #and proof stren+th& of a fastener. 'specially in critical situations, you should never reuse a fastener unless you are certain the fastener has neve r been yielded.
1.1 Bolt Preload Measurement 0f a more accurate answer for bolt preload is needed than discussed above, the specific combination and lubricant would have to be measured instead of calculated. 2easurement methods are +enerally involved, time-consumin+, and expensive, and are beyond the scope of this article. But perhaps one of the simplest and least expensive methods, to test specific combinations and lubricants, is to measure the installed fastener with a micrometer, if possible, and compute torque coefficient $ as follows, per *hi+ley,op. cit., p. 671, para. . $ ! T "#' G delta %& #'q. 7& where T ! bolt installation torque, ! bolt +rip len+th, ' ! bolt modulus of elasticity, G ! bolt cross-sectional area, % ! bolt nominal shan diameter, and delta ! measured bolt elon+ation in units of len+th.
