influence of tightening procedures and lubrication

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Influence of tightening procedures and lubrication conditions on titaniumscrew joints for lightweight applications

Dario Croccolo n, Massimiliano De Agostinis, Nicol �o Vincenzi

University of Bologna—DIEM, V.le Risorgimento 2, 40136 Bologna, Italy

a r t i c l e i n f o

Article history:

Received 28 February 2012

Received in revised form

4 May 2012

Accepted 13 May 2012Available online 2 June 2012

Keywords:

Friction coefficient

Titanium screw

Re-tightening

Lubricant

a b s t r a c t

In recent years, the need for lighter vehicles led to the widespread of lightweight alloys, such as

titanium, also in the field of threaded fasteners. Unluckily, the replacement of steel bolts with titanium

ones, usually suggested because of their favourable ratio between strength and weight, is not quite

straightforward. The coefficient of friction, a key parameter in bolted joints design, changes drastically

when switching from steel to titanium. Some results concerning the frictional behaviour of bolted

joints involving titanium screws are here presented: friction and torque coefficients were calculated,

according to ISO 16047, for joints made up of a hexagon socket head screw made of titanium alloy

(Ti–6Al–4V), a bush made of aluminium alloy (EN AW 7075 T6) and a steel nut (ISO 4032). Data were

collected by performing several tightening tests on ad-hoc designed specimens, which allowed the

evaluation of the different tribological behaviour of the same joint under three different conditions of

lubrication (dry, Teflons added oil, and ceramic paste). 20 repeated tightenings (re-tightenings) have

been analysed in order to simulate some maintenance operations. The DOE method was applied to

manage the tests, while the results were analysed by the ANOVA and P-value methods. Out of the two

lubricants examined, the ceramic paste showed the best results in terms of friction coefficients

constancy throughout the re-tightening operations, as well as the best protection of the thread and

underhead surfaces against wear.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, lightweight design is increasingly pursued in theautomotive and aeronautical applications as it helps fulfillingenvironmental pollution regulations, fuel saving requirementsand the demand for better dynamic performances. Weight savingscan be realized by a careful optimisation of structural compo-nents, which include fastening and joining systems. Among these,threaded fasteners are often the preferred choice because theyoffer the possibility to repeat assembly and disassembly opera-tions for the maintenance of joined components. The bolt pre-loading force is normally achieved by using a torque wrenchapplied to the head or to the nut so that the tribological aspects ofthe tightening phase are critical to define the actual torque-preloading relationship [1–3]. The tightening torque is mostlyconsumed in overcoming two friction components: the under-head friction due to the sliding of the fastener head on the flangesand the thread friction between the male and female threads.

The residual torque component produces the fastener tension bygenerating the joint clamping force. Inaccuracies in determiningthe friction components may lead to an overestimation or under-estimation of the bolted joint performances. The torque-preload-ing relationship is often simplified by using a constant K, knownas torque coefficient or nut factor. The expression for the torquecoefficient is reported in Eq. (1), where T (Nmm) is the input(total) tightening torque applied to the fastener, F (N) is theneeded preloading force and d (mm) is the nominal screwdiameter.

T ¼ KFd ð1Þ

Some authors [4,5] suggest that an approximated or meanvalue of K¼0.20 could be used, which holds true only in thepresence of screws, nuts and flanges made of steel. For thisreason, some recent European standards prescribe that theappropriate torque coefficient must be provided by the boltmanufacturer [6–8]. Bickford [9] indicates some mean values ofthe torque coefficient for various combinations of joint materialsand surface conditions; however, the scatter is too great toprovide a reliable value, especially for critical joints and, further-more, only steel screws are considered. Motosh [10] and VDI 2230[11] propose the full torque-preload relationship, for metric (ISO)thread profile, reported in Eq. (2) and obtained as the addition of

Contents lists available at SciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/triboint

Tribology International

0301-679X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.triboint.2012.05.010

Abbreviations: ANOVA, Analysis of Variance; DOE, Design of Experiment;

FEM, Finite Elements Methodn Corresponding author.

E-mail address: [email protected] (Dario Croccolo).

Tribology International 55 (2012) 68–76


three different contributions (pitch, threads and underhead).

T ¼ F½0:16Pþ0:58mthd2þ0:5mbDb� ð2Þ

P (mm) is the thread pitch, mth is the friction coefficientbetween male and female threads, d2 (mm) is the mean threaddiameter, mb is the underhead friction coefficient and Db (mm) isthe underhead mean diameter. By considering a M8�1.25 bolt(d2¼7.19 mm, Db¼11 mm) and a mean value for friction coeffi-cients mth and mb equal to 0.15, it is easy to verify that 88% of thetotal input torque T is consumed in overcoming friction [1].Despite the fact that the majority of bolted joints in mechanicalsystems are still steel screws, many kinds of lightweight materialshave been recently adopted for screws construction [12,13]. Sincethe use of threaded fasteners is considered worldwide to bean easy and simple way of joining components, sometimesdesigners do not take into account the changed boundary condi-tions correctly, when replacing conventional steel screws withlightweight ones, or simply when replacing the surface finishingof bolted components. In a previous paper [1], the authorsexamined several failures occurred on clamped joints (Fig. 1),due to the wrong estimation of friction coefficients. Such com-ponents belonged to front motorbike suspensions [14–16] andwere made up of one or two zinc plated steel screws acting onaluminium alloy. The thread and the underhead regions could beanodised or spray-painted: the DOE methodology was applied todetermine reliable values for the friction coefficients (and there-fore for preloading forces) involved in the joints in order to avoidfailures.

In the present work, the authors apply a similar methodologyto some M8�1.25 socket head screws made of titanium alloy:because of the favourable ratio between mechanical strength and

density, titanium screws are eligible for applications that requirelow weights and high performances, as for example sports cars,where titanium screws are used to connect the wheel rim to thewheel hub (Fig. 2).

Moreover, titanium screws are sold as aftermarket specialparts, intended to replace steel screws on existing assemblies.Unfortunately, as indicated in next sections, the friction coeffi-cients relevant to titanium screws are considered higher thanthose of steel ones. Since the wrong estimation of frictioncoefficients may lead to catastrophic repercussions [17–19] thereplacement of steel screws with titanium ones is not quitestraightforward because the same tightening torque prescribedfor steel screws would produce a lower clamp force if titaniumbolts are adopted. In order to preserve the preloading force it is,therefore, necessary to increase the torque applied during thetightening operation, even if the high values of friction coefficient,especially in the case of unlubricated surfaces, can lead to thesocket head failure shown in Fig. 3.

In this work, the authors examined the frictional behaviour ofa bolted joint made up of three elements, namely titanium screw,aluminium underhead and steel threads. Such combinationapproximates the behaviour of the joint of Fig. 2, and the resultscan be useful for car manufacturers. In order to fully exploit thecapabilities of lightweight alloys and to avoid excessive wear,lubrication during the assembly is suggested by standards [20]:therefore the authors assessed the frictional behaviour of the joint

Nomenclature

Aeq Cylindrical equivalent section of the specimen (mm2)At Screw tensile stress area (mm2)d2 Pitch (mean) diameter of the thread, d2¼d�0.649 � P

(mm)d3 Core (minor) diameter of the thread, d3¼d�1.227 � P

(mm)dt Stress diameter of the thread, dt¼d�0.938 � P (mm)Db Diameter of bearing surface under nut or bolt head for

friction (theoretical value) (mm)P Thread pitch (mm)E Young’s modulus (MPa)F Clamp force (N)FC Preloading force of the specimen (N)

K Torque coefficient (dimensionless)T Total torque (Nm)Tth Thread torque (Nm)eC Axial strain of the specimen (dimensionless)mth Coefficient of friction between threads

(dimensionless)mb Coefficient of friction between bearing surfaces under

nut or bolt head (dimensionless)mtot Coefficient of total friction (dimensionless)sax Axial preloading stress related to F (MPa)sEQ Equivalent von Mises stress acting on the screw shank

during the tightening (MPa)t Shear stress related to Tth (MPa)Sp Proof stress (MPa)SR Stress ratio (dimensionless)

Fig. 1. Failure occurred on a clamped joint connecting the front axle to the axle

bracket of a motorbike. Fig. 2. Car wheel assembly with titanium screw.

D. Croccolo et al. / Tribology International 55 (2012) 68–76 69


when different lubricants are applied to the mating parts beforetightening. The evolution of friction coefficients over twentyassembly and disassembly operations was also observed duringthe experimentation in order to simulate the maintenance opera-tions due to periodical tires substitution.

2. Methodology and results

In order to evaluate the friction coefficients accurately, and todevelop a mathematical expression, the Design of Experiment(DOE) method was applied. After some screening analyses, a fullfactorial plane, characterised by 2 variables with 3 levels each,was prepared. In order to reduce the influence of noise (experi-mental error) and any non-investigated factors three replicaswere carried out [1]. Then, a total of 3�32

¼27 experimentalobservations were performed and used in the DOE, whose para-meters are indicated in Table 1. Due to the experimental observa-tions needed in correspondence of the 20th tightening operationfor the level 2 (see Table 1), a total of 27/3�20¼180 differenttests were performed.

As already shown in [1] and according to VDI 2230 [11] andISO 16047 [21], Eq. (2) is rearranged into Eq. (3), considering bothmth and mb equal to mtot in order to derive the overall frictioncoefficient of the bolt/nut assemblies.

T ¼ F 0:16Pþ0:58mtotd2þ0:5mtotDb

� �mtot ¼

T=F�0:16P

0:58d2þ0:5Dbð3Þ

Each test planned by the DOE must provide a value of theoverall friction coefficient mtot (Eq. (3)). In order to calculate mtot

some specific specimens, sharing the key parameters of the actualcomponents involved in the wheel-rim joint, were designed andrealized (Fig. 4).

The screw [Poggipolini S.r.l.] is a hexagon socket head M8�1.25 with a length L¼60 mm, made up of Ti–6Al–4V alloy rolledafter heat treatment and without any surface coating (roughnessRa¼0.8 mm). Mechanical properties can be summarised by anyield strength in the range 830–880 MPa, an ultimate strength inthe range 900–1.050 MPa, Young’s modulus of 105 GPa, minimumelongation at break 10%, mass density 4.4 g/cm3, Vickers hardness

320 HV. In terms of mechanical strength titanium screws canbe considered similar to 10.9 steel screws. Ti–6Al–4V is themost commonly used titanium alloy, applied to many aerospaceapplications too [22]. The bush is made up of EN AW 7075 T6aluminium alloy, without any surface coating (roughnessRa¼1.6 mm); such aluminium alloy is widely used for manufac-turing the cone washer which is inserted between the screw andthe wheel rim, as reported in the scheme of Fig. 2. Although lesscommon, other aluminium alloys as, for example, EN AW 2024 T3could be used to realise the washer; moreover the EN AW 7075 T6alloy is widely used in front motorbike suspensions such as thosereported in Fig. 1. The nut is a ISO 4032–M8�1.25�8, withoutany surface coating. The specimen has two strain gauges applied1801 apart from each other, in order to clean the signal fromundesired bending moments due to a possible misalignmentbetween the bush and the screw axes. The lateral cuts allowclamping the specimen in a standard workbench vice: at the sametime they prevent the nut from rotating with respect to thespecimen. Each specimen has two HBM 1-LY43 strain gauges witha 3 mm grid and 120 O resistance, arranged in a half bridgeconfiguration and connected to a Vishay P-3500 Strain Indicatorby means of which the bridge completion and the calibrationare done. The total torque T is applied by means of the digitaltorque wrench Torcotronic II 8455-120 produced by Gedore. Themeasurement range of the torque wrench is between 10 and120 Nm. The lubricants [Interflon BV] used for the experimenta-tion are an industrial oil fortified with Teflons (Fin Lube EP Plus)and a ceramic paste suitable for high temperature applications(HT 1200) (Fig. 5).

The clamp force F is evaluated by means of the strain gaugesplaced on the external surface of the specimen. The compressionforce FC (Eq. (4)) acting on the specimen is equal, in magnitude, tothe preloading force acting on the screw (the system works likeseries of springs during the tightening phase).

9FC9¼ F ¼ 9eC9EAeq ð4Þ

E [MPa] is Young’s modulus of the aluminium specimen (69,000 MPa)and Aeq (mm2) is the cylindrical equivalent cross section of thecompressed region, when the external diameter of the bush (DA¼

15 mm) exceeds the bolt head diameter (dw¼13 mm) as indicated inthe drawing of Fig. 4.

Aeq can be easily calculated by means of the formula proposedby [23] and reported in Eq. (5), as a function of the internaldiameter of the specimen dh¼8.5 mm, the length of the specimen

Fig. 3. Titanium screw assembled on an aluminium test specimen (Left) and

failure of the hexagon socket head.

Table 1The Design of Experiment (DOE) parameters: variables and levels.

Variable Level 0 Level 1 Level 2

A. Tightening number 1st (A¼0) 10th (A¼1) 20th (A¼2)

B. Lubrication Dry (B¼0) PTFE Oil (B¼1) Ceramic paste (B¼2)

Fig. 4. Test specimen.

D. Croccolo et al. / Tribology International 55 (2012) 68–7670


lk¼40 mm and of the two parameters DA and dw.

Aeq ¼p4ðd2

w�d2hÞþ

p8

dwðDA�dwÞ

ffiffiffiffiffiffiffiffiffiffiffiffilkUdw

D2A

3

sþ1

" #2

�1

24

35¼ 120:83 mm2

ð5Þ

Since the specimen was expressly designed to be very similar to athin bush, the equivalent cross section Aeq can be consideredequal to the actual cross section A reported in Eq. (6): thedifference is negligible.

A¼p4ðD2

A�d2hÞ ¼ 120 mm2 � Aeq ð6Þ

Other approaches [11] can be, anyway, used in order todescribe the compressive behaviour of clamped parts.

During the screening tests, the authors double checked thatthe ratio between T and F remained constant for tightening torquevalues T ranging between 10 Nm and 50 Nm (see Fig. 6).

A test was performed on a new specimen (1st tightening) withdry surfaces. For subsequent tests it was decided to set thetightening torque at T¼25 Nm, because this value is about in

the middle of the measurement range of the torque wrench and,moreover, it is low enough to avoid the overcoming of the screwyield point due to an excessive clamp load when lubricants areapplied. According to the DOE methodology, the experimentaltests were randomized [24]: the preloading force F was derivedvia strain gauges whereas both the overall friction coefficient mtot

(Eq. (3)) and the torque coefficient K (Eq. (1)) were calculated asfunctions of the variables and levels reported in Table 1. Once thevalues of mtot and K were calculated, their results were studied byapplying the ANalysis Of VAriance (ANOVA) [1,24,25]. Suchtechnique is based on a statistical approach and allows evaluatingthe effect of each variable and of their interactions, in order toidentify the variables and interactions that are significant todefine the friction coefficients value. By means of the softwareStagraphicss Plus, Release 5.1, the ANOVA table was generatedand the P-value test was done (see Table 2). All the five effects(singles and interactions) examined had P-values less than 0.05,indicating that they are significant in changing friction coeffi-cients with a confidence level equal to 95%. Therefore, themathematical models for mtot and K were found and they arepresented in Eqs. (7) and (8) respectively. In such expressions

Fig. 5. T–F diagram for torque values between 10 Nm and 50 Nm, unlubricated surfaces.

Fig. 6. Friction coefficient mtot (mean, maximum and minimum values) versus tightening number for DRY surfaces (B¼0).



A and B represent the DOE parameters (see Table 1) that canassume the values 0, 1 or 2, depending on the number oftightenings (A¼0 for the first tightening, A¼1 for the 10thtightening and A¼2 for the 20th tightening) and on the lubrica-tion condition (B¼0 for the dry surfaces, B¼1 for EP oil treatmentand B¼2 for HT1200 paste treatment); the presence of theirsingle and combined effects depends on the effectiveness ofparameters which can be retrieved by their P-value reported inTable 2.

Both mtot and K coefficients do not allow evaluating thescrew stress, they can only relate the tightening torque with theclamp force.

mtot ¼ 0:240þ0:084A�0:156B�0:016A2�0:030ABþ0:038B2

ð7Þ

K ¼ 0:313þ0:100A�0:184B�0:019A2�0:036ABþ0:044B2

ð8Þ

Looking at Table 2 and at Eqs. (7) and (8), it can be appreciatedhow lubrication (B) is the most significant parameter. The evolu-tion of the total friction coefficient mtot versus the tighteningnumber, in the case of dry surfaces (B¼0), is reported in Fig. 6. InFigs. 7 and 8 the same evolution is shown in the cases of EP oil(B¼1) and HT1200 paste (B¼2) lubricated surfaces, respectively.It is worth highlighting that each lubricant was only appliedbefore the first tightening: the specimens were not re-lubricatedduring the 20 re-tightenings. In each diagram, a grey box high-lights the mean value of mtot, while the scatter bands show theextreme values recorded in the experimental campaign. Thedashed line represents the values of mtot calculated by means ofEq. (7) once the lubrication parameter B is set equal to 0, 1 or 2 fordry, EP oil and HT1200 paste respectively. Eq. (7) was verified to

Table 2Example of ANOVA Table results for mtot.

Effect (interaction) Sum of squares SS DoF Mean Square

MS¼SS/DoF

P-value

A—Tightening number 0.0098 1 0.0098 0.000

B—Lubrication 0.2178 1 0.2178 0.000

AA 0.0015 1 0.0015 0.038

AB 0.0108 1 0.0108 0.000

BB 0.0086 1 0.0086 0.000

Error 0.0062 21 0.0003

Fig. 7. Friction coefficient mtot (mean, maximum and minimum values) versus tightening number for EP Plus oil lubricated surfaces (B¼1).

Fig. 8. Friction coefficient mtot (mean, maximum and minimum values) versus tightening number for HT1200 paste lubricated surfaces (B¼2).



be effective for any arbitrary value of the tightening numberparameter A between 1 and 2.

Referring to the left column of Fig. 6 (first tightening) it can benoticed that mtot takes a value of 0.2270.02 in the case of drysurfaces, which can be considered quite high. Moreover, Fig. 6shows a noticeable growth of mtot along the whole series oftwenty tightenings (þ41% and þ59% in correspondence of the10th and 20th tightening, respectively). Both Figs. 7 and 8 showthat the addition of a lubricant brings the mean friction coeffi-cient down at first tightening: the lowest values of mtot are foundfor the HT1200 paste. Throughout the re-tightening operations,the HT1200 paste shows no increase of mtot while a sensibleincrease can still be observed in the case of EP Plus oil application(þ33% and þ42% in correspondence of the 10th and 20thtightening, respectively). Of utmost importance is the fact thatthe scatter is negligible if the HT1200 paste is used: so use ofpaste means that the clamp force is roughly constant.

The thread friction coefficient (mth) and the underhead frictioncoefficient (mb), which combine to bring about the mean friction

coefficient (mtot), were measured as well, but they are notreported here for the sake of brevity. In order to retrieve thethread contribution, by nulling the underhead contribution offriction, a thrust bearing was applied under the screw head asindicated in Fig. 9. The thread friction coefficient (mth) andunderhead friction coefficient (mb) were then calculated fromEq. (2) following the indications of ISO 16047.

During such test, and only in the case of EP Plus oil addition,the stick-slip phenomenon was observed on about 20% of theperformed tightenings (see the embedded video) so that, in thiscase, it is difficult to obtain a reliable value of mth. It is known fromthe literature [27] that stick-slip may appear in the presence ofhigh pressure, low sliding velocity, when the surfaces in contacthave no coating and the joint is lubricated with mineral oil: suchconditions match very well to the case under investigation. It isworth remarking that the tests performed without the thrustbearing never have shown the stick-slip phenomena and that theHT1200 paste avoided any stick-slip occurrence also when thethrust bearing was applied. As indicated in the diagram of Fig. 10,the preloading force decreases drastically from the first to thetwentieth tightening in the unlubricated specimens, providedthat the tightening torque be constant.

Supplementary material related to this article can be foundonline at http://dx.doi.org/10.1016/j.triboint.2012.05.010.

This occurrence is due to the wearing and the scratching of thethread and underhead surfaces when the re-tightening operationsare carried out [1,28]. Both lubricants tested produce moreconsistent values of the preloading force since their protectivefilm preserves the surfaces from wear. Such behaviour is muchmore pronounced in the case of HT1200 paste, where thepreloading force shows a small increase during the twentyoperations. The former statement can be easily confirmed lookingat Fig. 11, where the different amount of wear on the screwthreads after twenty re-tightening operations can be appreciated,by comparing the presence of HT1200 paste (a) with the absenceof any lubrication (b).

3. Discussion

During the tightening operation the screw must produce therequired axial preloading force by means of an imposed tighten-ing torque T. By analysing the tensile state present on the screwshank during the tightening it is possible to observe that besidesFig. 9. Thrust bearing under the screw head for mth evaluation.

Fig. 10. Preloading force F versus tightening number (T¼25 Nm).



the axial preloading stress sax (MPa) there is the additional shearstress t (MPa) related to the portion of torque Tth that crosses theunderhead, as reported in Fig. 12.

It is, therefore, possible to calculate the equivalent axial stresson the shank sEQ (MPa), by applying the von Mises criterion,according to Eq. (9), where dt (mm) is the stress diameter relatedto the thread stress area At (Fig. 12), and to compare such valuewith the screw yield strength.

sEQ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

axþ3t2q

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF

At

� �2

þ3Tth

Wt

� �2s

¼

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4F

pd2t

" #2

þ316Fð0:16Pþ0:58mtotd2Þ

pd3t

" #2vuut

ð9Þ

The equivalent stress depends on the friction coefficient mtot. Inorder to fully exploit the strength of the screw, the equivalentstress sEQ should be as close as possible to the axial preloadingstress sax. In other words, the torsional (undesired) stress shouldbe as low as possible: this condition is achieved leveraginglow values of friction coefficient. The three different lubricationconditions for titanium screws were, therefore, compared by cal-culating the stress ratio SR¼sEQ/sax given by the ratio betweenthe equivalent stress and the axial preloading stress; results arereported in Fig. 13.

Automotive companies usually specify, for bolted joints, theacceptable coefficient of friction range with the aim of obtaining alow preload scatter. For example, German manufacturers specifythe range 0.09–0.14 [28] that implies a stress ratio SR limited to1.28. Similarly, French manufacturers specify the range 0.12–0.18[28] that means having a stress ratio SR limited to 1.39. In TableA5 of VDI 2230 [11] (Friction coefficient classes with guide valuesfor different materials/surfaces and lubrication states in boltedjoints) it is suggested that friction coefficients shall be between0.08 and 0.16, with the higher value roughly corresponding to astress ratio SR of 1.33, represented by the dashed grey lineindicated in Fig. 13. The diagram in Fig. 13 strongly advisesagainst the use of titanium screws without lubrication (thisadvice can be found, for instance, in the Aerospace series standardEN 2491 [20]). As a matter of fact, by equating sEQ to the materialyield stress or to the proof stress Sp (MPa) equal to 90% ofyield stress as suggested in VDI 2230, it is possible to evaluatethe maximum preloading force during the tightening phase asF_max¼(At � Sp)/SR. Engineering values of the parameter 1/SR fortitanium screws are summarised in Table 3 (handbooks typicallysuggest for tightening the value F¼0.70 �At � Sp). The resultspresented in Table 3 indicate that the torsional stress due to highcoefficients of friction limits the preloading capability of dryscrews: in order to reach the value 0.70 �At � Sp lubrication ismandatory.

Future investigations will analyse the frictional behaviour oftitanium screws clamped on different lightweight materials (i.e.magnesium, titanium and CFRP). It is necessary to remark on theneed for this kind of experimentation because the standardfrictional tests, such as pin-on-disc, are usually based on lowpressures and high sliding velocities between the tested materi-als, at least if compared to the bolt tightening phase. In the case ofscrews a very different situation can be found: (i) the slidingvelocity is limited to low values; (ii) looking at the FEM contourplot of the tested titanium screws reported in Fig. 14, the pressuredistribution in the underhead or in the thread is far from aconstant or regular distribution [29]. The FEM calculation wasperformed with ANSYS R.12, using a simplified axisymmetricmodel, consisting of about 155,000 nodes, with triangular ele-ments (PLANE183 in the ANSYS nomenclature). The contactformulation adopted here was a pure penalty frictional contact(CONTA172 and TARGE169 ANSYS contact elements) as pre-viously done in another work dealing with contact problems bythe same authors [30], while the material behaviour was linearelastic and the load was purely axial. Up to now, a mean value of

Fig. 11. Effect of 20 re-tightenings on engaged threads (a): screw lubricated with HT1200 paste (b): dry screw.

Fig. 12. Tensile state on the screw shank during the tightening.



pressure is considered and a mean value for friction coefficient iscalculated, according to previous sections, whereas future inves-tigations must take into account the local value of frictiondepending on the local pressure distribution.

4. Summary and conclusions

Friction and torque coefficients were calculated for somebolted joints made up of a hexagon socket head screw made oftitanium alloy, a bush made of aluminium alloy (underhead) anda steel nut. Data were collected by performing a number oftightening tests on ad-hoc designed specimens, which allowedthe evaluation of the different tribological behaviour of the samejoint under three different conditions of lubrication. In order tosimulate maintenance operations, twenty repeated tightenings(re-tightenings) were analysed. The DOE method was applied,while the results were analysed by the ANOVA and P-valuemethods. The most expected outcome of the study is the strongdependence of friction on the lubrication conditions and on thenumber of re-tightenings, although the addition of HT1200 pastebefore the first tightening is able to keep constantly the meanfriction coefficient at low values throughout the whole number ofre-tightenings. This is due to the capability of the paste to protectthe thread and underhead surfaces from wear. From this study itcan be learned that titanium screws do need lubrication in anycase, and especially when coupled with aluminium components.Such a materials combination shows, in fact, a remarkablesensitivity to wear, perhaps because of the high local pressure,the poor surface hardness and the low compressive strength ofaluminium, combined with a good compatibility between the twomaterials (see Rabinowicz charts). Since the exact knowledge oflocal friction coefficients is crucial in order to fully exploit thematerials strength, especially in lightweight applications, future

investigations with the aim to find local friction laws, related tolocal contact pressure and sliding velocity will be presented in ashort time. The findings proposed herein can be used during thedesign phase of bolted joints comprising titanium bolts, as well asfor maintenance operations reference, in order to estimate the

Fig. 13. SR¼sEQ/sax as a function of the number of tightenings, for the three different lubrication conditions.

Table 3Maximum preloading forces F_max for titanium Ti–6Al–4V screws.

1st tightening 10th tightening 20th tightening

Dry (unlubricated) 0.63 �AtSp 0.55 �AtSp 0.51 �AtSp

Lubricated with EP plus oil 0.82 �AtSp 0.75 �AtSp 0.74 �AtSp

Lubricated with HT1200

paste

0.88 �AtSp 0.86 �AtSp 0.89 �AtSp

Fig. 14. Stress and pressure distribution (F¼15 kN, mtot¼0.08) in the surfaces in

contact: (a) underhead, (b) first engaged thread.



actual preloading force acting on the joint when different kinds oflubrication are applied.

Acknowledgements

The authors would like to gratefully acknowledge Mr. FedericoBizzi and Mr. Stefano Poggipolini of Poggipolini S.r.l., Mr. AlessandroGrelli of Interflon Italia S.r.l., Mr. Marco Arcaleni and Mr. RiccardoBonomi of Bonomi Eugenio S.p.A. for their fundamental contribu-tion to this research.

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