Frictional Behavior of Steel-PTFE Interfacesfor Seismic Isolation
M. DOLCE∗, D. CARDONE and F. CROATTODiSGG, University of Basilicata, Macchia Romana Campus, 85100, Potenza, Italy∗Corresponding author. Tel: +390971205052; Fax: +390971205052, E-mail:[email protected]
Received 17 October 2004; accepted 6 December 2004
Abstract. The widespread use of sliding bearings for the seismic isolation of structuresrequires detailed knowledge of their behavior and improved modeling capability under seis-mic conditions. The paper summarizes the results of a large experimental investigation onsteel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure,air temperature and state of lubrication on the mechanical behavior of steel-PTFE slidingbearings. Based on the experimental outcomes, two different mathematical models have beencalibrated, which are capable of accounting for the investigated parameters in the evalua-tion of the sliding friction coefficient. The first model is basically an extension of the modelproposed by Constantinou et al. (1990) Journal of Earthquake Engineering, 116(2), 455–472,while the second model is derived from the one proposed by Chang et al. (1990) Journal ofEngineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a functionof bearing pressure and air temperature are presented for lubricated and non-lubricated slid-ing surfaces. Predicted and experimental results are finally compared.
Steel–PTFE sliding bearings have been widely used in the past to accom-modate thermal movements and effects of pre-stressing, creep and shrink-age in bridges. More recently, they have been proposed as part of seismicisolation systems, to support the weight of the structure, while relying uponseparate mechanisms, to provide the system with re-centring and additionalenergy absorbing capability.
Several sliding isolation systems with restoring force have been pro-posed. Some of them have reached the stage of implementation, such as theResilient-Friction Base Isolation System (Mostaghel, 1984), based on theelastic properties of rubber, the SMA Isolation System (Dolce et al., 2000),based on the superelastic properties of shape memory alloys, and the Fric-tion Pendulum System (Zayas et al., 1987), which exploits an articulatedslider moving on a spherical surface to provide restoring capability. Themost important advantage in using sliding isolation systems with (weak)
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restoring force is that the structural response is little sensitive to variationsin the frequency content of the earthquake.
In Italy a different approach has been followed (Dolce, 2001). A verylarge number of bridges, indeed, have been equipped with elasto-plastic iso-lation systems, consisting of lubricated sliding bearings and hysteretic steeldampers. Such systems are able to limit the force transmitted by the deckto piers and abutments to a predefined level, almost independent from theintensity and spectral content of the seismic excitation. The drawbacks arethe large dispersion in the peak displacements and the occurrence of per-manent displacements after strong earthquakes.
Many numerical analyses of the seismic response of structures equippedwith steel–PTFE sliding isolation systems have been carried out (Mostagheland Tanbakuchi, 1983; Fan et al., 1988). In all these studies, as well asin the current design practice, it is assumed that the friction coefficientcomply with the Coulomb friction law (i.e. friction remains constant dur-ing sliding). Actually, experimental observations (Constantinou et al., 1987;Hwang et al., 1990; Mokha et al., 1990), pointed out that the frictioncoefficient increases more than linearly while increasing sliding velocity,while it decreases with the increase of the contact pressure. Temperatureand number of sliding reversals also play a not negligible role (Tyler, 1977).
An accurate mathematical model of the frictional behavior of steel–PTFE sliding bearings has been developed in (Constantinou et al., 1990).It is based on the viscoplasticity theory (Wen, 1976), and is referred toas modified viscoplastic model. Its main characteristic is the dependenceof the friction coefficient on sliding velocity and bearing pressure, throughan exponential analytical law. The Constantinou’s model has been imple-mented in the structural analysis program SAP-2000 Nonlinear (SAP-2000,2002), as the Friction-Pendulum Isolator NLLink element. Applications ofthe exponential model in the analysis of a sliding isolation system havebeen reported in (Constantinou et al., 1990; Mokha et al., 1993; Deb andPaul, 2000), mainly with the scope of evaluating the effects of bearing pres-sure, sliding velocity, breakaway friction and bi-directional motion on theseismic response of base-isolated buildings, compared with the predictionsof the Coulomb’s model. An interesting comparison between experimentaland numerical results is reported in (Tsopelas et al., 1996), with referenceto a bridge structure.
The Constantinou’s model is a phenomenological model, being derivedfrom the observation of experimental results. An evolution of theConstantinou’s model, based on the tribology theory, has been recentlyproposed in (Takahashi et al., 2004) to describe the frictional behavior ofPTFE–steel interfaces at the microscopic level.
A comprehensive program of experimental tests has been carried out atthe laboratory of the University of Basilicata on steel–PTFE interfaces, in
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 77
order to fully investigate the effects of sliding velocity, contact pressure, airtemperature, number of cycles and state of lubrication on the mechanicalbehavior of steel–PTFE sliders. Based on the experimental outcomes, twomathematical models of their frictional behavior, for conditions of interestin seismic isolation, have been developed and calibrated. The first modelis basically an extension of the model proposed in (Constantinou et al.,1990), while the second model is derived from the one proposed in (Changet al., 1990). In this paper, the main results of the experimental tests aredescribed. Model predictions and experimental results are then compared.
2. Experimental Set up and Procedure
The experimental program on steel–PTFE interfaces had two specific objec-tives: (i) investigating the variability of the sliding friction coefficient whilevarying contact pressure, velocity, air temperature, displacement amplitudeand state of lubrication of steel–PTFE interfaces, (ii) developing and cali-brating a numerical model of the mechanical behavior of steel–PTFE slid-ing bearings.2.1. Materials
The materials used were as follows:• Unfilled PTFE pads obtained from a 5.45 mm thick sheet with dimpled
recesses, whose dimensions and pattern are shown in Figure 1. The func-tion of the dimple recesses is to retain the grease and to gradually intro-duce it between the sliding interfaces, during wear of PTFE.
• Stainless steel plates (AISI 316/L) of 3 mm thickness, polished to mirrorfinish, with less than 0.1 µm surface roughness.
• Silicone grease, of the type normally used in the bearing manufacturing.
Figure 1. Details of PTFE dimpled recesses.
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2.2. Test apparatus
The testing apparatus is schematically shown in Figure 2. A central steelplate is laterally finished with two polished stainless steel plates (300 mmby 45 mm dimensions) and sandwiched between two couples of 40 by25 mm PTFE pads, with 5.45 mm thickness. The PTFE pads are placedinto recesses of two lateral steel plates. The protrusion of the pads was2.6 mm in the unloaded condition.
The PTFE–steel interfaces are compressed by a 50 kN hydraulic jackand four pre-stressing steel rods. The lateral steel plates are attached to areaction frame, while the central steel plate is driven by a 10 kN Instrondynamic actuator, with ±125 mm stroke. The dynamic actuator is equippedwith a 63 lit/s controller valve, a ±10 kN load cell and a ±125 mm inter-nal inductive transducer. The above said test arrangement is placed inside athermal room, working in −30 ◦C/+80 ◦C temperature range. The air tem-perature is controlled by a K-type thermocouple.
Figure 2. Testing apparatus.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 79
2.3. Test program
More than 300 tests have been carried out on steel–PTFE interfaces with9.36, 18.72 and 28.1 MPa bearing pressures, −10, 20 and 50 ◦C air temper-atures, from 1mm/s to about 300 mm/s sliding velocities, from 10 to 50 mmdisplacement amplitudes. Both lubricated and non-lubricated steel–PTFEinterfaces were tested. In most of the tests, the motion was sinusoidal, withspecified amplitude and frequency. Furthermore, a number of tests wereconducted with constant velocity motion (i.e. saw-tooth displacement–timehistory). The two types of tests produced almost identical results for thesame peak velocity of sliding.
Table I summarises the whole experimental program. As can be seen,nine series of tests have been carried out. Each series consisted of 16tests, all at the same air temperature and contact pressure. The contactpressure was progressively increased from one series to another, while keep-ing the temperature constant. Every three series of tests the PTFE padswere replaced by new ones.
Table I. Test program.
Test Interfacesa T b(◦C) P c (MPa) dd f e Wavef vg Cycles CDh
No. (mm) (Hz) (mm/s) No. (mm)
1 L/P −10/20/50 9.36/18.7/28.1 50 0.05 TR. 10 5 10002 L/P −10/20/50 9.36/18.7/28.1 50 0.2 TR. 40 5 20003 L/P −10/20/50 9.36/18.7/28.1 50 0.5 TR. 100 5 30004 L/P −10/20/50 9.36/18.7/28.1 50 1 TR. 200 5 40005 L/P −10/20/50 9.36/18.7/28.1 10 0.05 SYN. var. 5 42006 L/P −10/20/50 9.36/18.7/28.1 10 0.2 SYN. var. 5 44007 L/P −10/20/50 9.36/18.7/28.1 10 0.5 SYN. var. 5 46008 L/P −10/20/50 9.36/18.7/28.1 10 1 SYN. var. 5 48009 L/P −10/20/50 9.36/18.7/28.1 25 0.05 SYN. var. 5 5300
10 L/P −10/20/50 9.36/18.7/28.1 25 0.2 SYN. var. 5 580011 L/P −10/20/50 9.36/18.7/28.1 25 0.5 SYN. var. 5 630012 L/P −10/20/50 9.36/18.7/28.1 25 1 SYN. var. 5 680013 L/P −10/20/50 9.36/18.7/28.1 50 0.05 SYN. var. 5 780014 L/P −10/20/50 9.36/18.7/28.1 50 0.2 SYN. var. 5 880015 L/P −10/20/50 9.36/18.7/28.1 50 0.5 SYN. var. 5 980016 L/P −10/20/50 9.36/18.7/28.1 50 1 SYN. var. 5 10,800aState of stainless steel–PTFE interfaces : L = lubricated, P = Pure.bAir temperature.cContact Pressure.dDisplacement amplitude.eFrequency of loading.f Displacement profile: TR = triangular, SYN = sinusoidal.gSliding velocity: var = variable.hCumulative distance.
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Triangular (saw-tooth) tests were carried out at constant displace-ment amplitude (50 mm), while increasing the sliding velocity from 10 to200 mm/s. In the sinusoidal tests, the displacement amplitude was variedfrom 10 to 50 mm, while increasing the frequency of loading from 0.05 to1 Hz, thus producing peak sliding velocities ranging from 1 to 300 mm/s.Five complete loading cycles were performed during each test. The cumula-tive distance during each series of test was approximately 10.8 m, as shownin Table I. Thus, a total distance of about 32.4 m was covered by each setof PTFE pads. The thickness of the PTFE pads was measured before test-ing and after their removal.
3. Experimental Results
3.1. Effect of type of test
Representative frictional force-displacement loops of the single interface areshown in Figures 3 and 4. They refer to tests conducted on non-lubri-cated interfaces under the same contact pressure (28.1 MPa), air tempera-ture (−10 ◦C) and displacement amplitude (50 mm), only differing for thewave form and the loading frequency. Figure 3 compares the frictionalbehavior exhibited by the PTFE–steel interfaces in (a) triangular and (b)sinusoidal tests at the same peak velocity, equal to 10 mm/s (i.e. test No. 1vs. test No. 13, according to Table I). Figure 4 refers to (a) triangular and(b) sinusoidal tests conducted at the higher peak velocities: 200 mm/s and300 mm/s, respectively (i.e. test No. 4 vs. test No. 16, according to Table I).For the sinusoidal tests, the peak velocity is defined as the average velocityin the displacement range corresponding to force levels greater than 95%of the maximum frictional force.
Two phenomena are clearly visible in the triangular tests, one at thestart of sliding, the other at every motion reversal. The first phenomenonis generally taken into account through the definition of a breakaway fric-tion coefficient, also known as static friction coefficient, to distinguish itfrom the sliding (kinetic) friction coefficient. The second phenomenon, gen-erally referred to as stick-slip, corresponds to a short duration increase ofthe frictional force, followed by a rapid decrease. Both the observed experi-mental phenomena can be related to (i) a momentary sticking of the inter-faces and to the (ii) acceleration impulse occurring at the start of the testand at every motion reversal, especially in the triangular tests.
The examination of Figures 3 and 4 clearly highlights the dependenceof the friction coefficient from sliding velocity. In each triangular test, theforce–displacement loops are practically rectangular, in accordance withfriction Coulomb’s law, but the friction force increases while increasing thefrequency of loading in the different tests. In the sinusoidal tests, on the
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 81
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Figure 3. Typical frictional force–displacement loops recorded during (a) triangularand (b) sinusoidal tests at low peak velocities (about 10 mm/s). Both tests were con-ducted on non-lubricated interfaces, under the same air temperature (−10 ◦C), contactpressure (28.1 MPa) and displacement amplitude (50 mm).
contrary, the friction coefficient varies during the motion, reaching its max-imum at the maximum velocity (i.e. at zero displacement). Furthermore thefriction coefficient tends to decrease during continuous loading cycles, thiseffect being related to self-heating of the sliding interfaces. Indeed, the rateof decrease of the friction coefficient is quite negligible in the tests al low
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Figure 4. Typical frictional force-displacement loops recorded during (a) triangularand (b) sinusoidal tests at very high peak velocities (>200 mm/s). Both tests were con-ducted on non-lubricated interfaces, under the same air temperature (−10 ◦C), contactpressure (28.1 MPa) and displacement amplitude (50 mm).
frequency (see Figure 3), while it is decidedly more pronounced (>20% infive cycles) in the tests at high frequency of loading (see Figure 4). Thephenomenon comes to an end in a few cycles, due to the attainment of anew thermal equilibrium with the ambient.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 83
3.2. Effect of sliding velocity
Figure 5 summarizes the results of all the tests on non-lubricated interfaces,in terms of sliding friction coefficient, i.e.:
µ= Fr
N(1)
where Fr is the frictional resistance of the sliding interfaces, and N is thenormal load applied during the tests, equal to 10, 20 and 30 kN, respec-tively.
In Figure 5, the sliding friction coefficient is reported as a function of(peak) velocity and contact pressure, for three different temperature values:(a) −10 ◦C, (b) 20 ◦C and (c) 50 ◦C, respectively. In the calculation of thesliding friction coefficient, reference was made to the second cycle of eachtest, by averaging the values of the friction force associated to both motionways. In Figure 5, the experimental data are represented by single points,while the curves correspond to analytical laws obtained from two differentfrictional models, as discussed below.
As can be seen, the sliding friction coefficient increases rapidly withvelocity, up to a certain velocity value, beyond which it remains almostconstant. This value is around 150 mm/s, regardless air temperature andbearing pressure.
The difference between maximum and minimum values of the slidingfriction coefficient (i.e. � = µmax − µmin, see Figure 6(a)) is larger at lowcontact pressures, being equal to about 12% at 9.36 MPa and less than 7%at 28.1 MPa. The air temperature has little influence on �. On the con-trary, the percent increment θ =�/µmin (see Figure 6(b)) tends to increasewhile increasing contact pressure, especially at medium-to-high tempera-tures, being of the order of 180% at 9.36 MPa, and 250% at 28.1 MPa.
In view of the use of steel–PTFE sliding bearings in seismic isolation,it is worth to remark that typical design values of displacement and fre-quency of vibration of isolated structures are between 100–200 mm and0.4–0.5 Hz, respectively. This means that the maximum sliding velocity,occurring in steel-PTFE bearings during an earthquake, ranges between160 mm/s and 400 mm/s. According to the experimental results, the slid-ing friction coefficient is practically constant for seismic applications, butsignificantly different from the friction coefficient in slow movements. Forthe sliding interfaces considered in this study, the sliding friction coefficientranges between 10% and 11% (depending on temperature) for a bearingpressure equal to 28.1 MPa, which is the closer experimental value to themaximum allowable contact pressure under seismic condition (i.e. 41 MPa)suggested in (AASHTO, 1999).
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Figure 5. Variation of the friction coefficient with sliding velocity, air temperatureand bearing pressure, for non-lubricated interfaces. Comparison between analyticallaws and experimental results. Air temperature equal to: (a) −10 ◦C, (b) 20 ◦C and(c) 50 ◦C.
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Figure 6. (a) Absolute and (b) percent increment of the sliding friction coefficient inseismic with respect to service conditions, as a function of contact pressure, for threedifferent air temperatures.
During its service lifetime, the sliding isolator acts as a usual slidingbearing, subjected to service load and thermal movements at very lowvelocities. The operating conditions of sliding bearing contained in var-ious codes (AASHTO, 1999), (BS 5400, 1983), (CEN 1337, 2000) arequite different. CEN considers lubricated steel–PTFE interfaces only, whileBS and AASHTO allow the use of both lubricated and non-lubricatedinterfaces. The maximum allowable contact pressure is assumed equal to24 MPa by AASHTO (in absence of specific wear tests), 45 MPa by BSand 60 MPa by CEN. For unfilled PTFE sliding against stainless steel with-out lubrication, the service friction coefficient suggested by AASHTO (inabsence of tests), for temperatures ≤ −25 ◦C, is equal to 15% at 10 MPaand 10% at 20 MPa (or more). At 20 ◦C, instead, the service limit state fric-tion coefficient is assumed equal to 6% at 10 MPa and 3% at 20 MPa (or
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more). It is worth to observe that the friction coefficient values obtainedin this experimental study, at the lowest sliding velocity (i.e. about 3 mm/s),substantially agree with the above mentioned code limits, being equal to: (i)8.9% at 9.36 MPa and −10 ◦C, (ii) 6.6% at 18.7 MPa and −10 ◦C, (iii) 6.5%at 9.36 MPa and 20 ◦C and (iv) 4.4% at 18.7 MPa and 20 ◦C.
3.3. Effect of contact pressure
As known (Mokha et al., 1990), the sliding friction coefficient of steel–PTFE interfaces reduces while increasing pressure. Based on the experimen-tal outcomes available (see Figure 5), the rate of reduction is practicallyconstant while increasing bearing pressure and quite insensitive to slidingvelocity and air temperature. As a matter of fact, by doubling the contactpressure (from 9.36 to 18.7 MPa) the friction coefficient reduces, on aver-age over the whole range of sliding velocities, by 24% (±3.4%) at −10 ◦C,up to 33.4% (±2.4%) at 50 ◦C. Similarly, by tripling the contact pressure(from 9.36 to 28.1 MPa) the friction coefficient reduces by 38.7% (±3.6%)at −10 ◦C, up to 47.2% (±3.9%) at 50 ◦C. It is worth to remark that thenegative variation of the friction coefficient with contact pressure reducesconsiderably the corresponding variation observed for the frictional forcewhen increasing the normal load.
3.4. Effect of air temperature
Figure 7 reports the friction coefficient at (a) very low (i.e. 8 mm/s) and(b) very high (i.e. 316 mm/s) sliding velocities, as a function of air temper-atures, for three different contact pressure values, namely: (i) 9.36 MPa, (ii)18.7 MPa and (iii) 28.1 MPa. Experimental data (points) and model predic-tions (curves) are compared.
The analytical curves reported in Figure 7 refer to the logarithmicmodel (see below), calibrated over the whole range of sliding velocities.This explains some inconsistencies between experimental and numericaldata, especially at low sliding velocity.
Based on the experimental results, the sliding friction coefficient decreaseswhile increasing air temperature, according to a second-order polynomiallaw (i.e. µ=a ·T 2 −b ·T + c, with a, b, c>0), whose expression is reportedin Figure 7, for 6 pressure–velocity couples of values. As can be noted, therate of reduction of the sliding friction coefficient is greater when passingfrom low-to-medium temperatures than when passing from medium-to-hightemperatures. Moreover, it depends on sliding velocity, while being practi-cally independent from contact pressure. At 8 mm/s (see Figure 7(a)), forinstance, the average rate of reduction of the sliding friction coefficient withtemperature is of the order of 0.77%/◦C when passing from −10 to 20 ◦C,
Figure 7. Sliding friction coefficient at (a) very low and (b) very high velocities (i.e. 8and 316 mm/s, respectively) as a function of air temperatures, for three different nor-mal pressure values (i.e. 9.36, 18.72 and 28.1 MPa, respectively). Comparison betweenexperimental results and model predictions.
while being of the order of 0.33%/◦C when passing from 20 to 50 ◦C. At316 mm/s (see Figure 7(b)), the rates of reduction decrease by about 2.5times.
To account for the changes in the friction resistance of steel–PTFE slid-ing isolation systems due to temperature variations, the AASHTO definestwo system property modification factors, λmax,t and λmin,t , which quantifythe effects of temperature variations on the nominal value of the frictioncoefficient at 20 ◦C reference temperature. They are defined as the ratio ofthe friction coefficient at the highest and at the lowest expected temper-ature (say 50 ◦C and −10◦C, respectively) to the friction coefficient at thereference temperature (20 ◦C). Specific tests lacking, AASHTO provides pre-determined values: λmax,t =1.2 and λmin,t =1, for non-lubricated steel-PTFEinterfaces operating at −10 ◦C and 50 ◦C, respectively. The corresponding
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experimental values drawn from the whole set of experimental data are 1.17(±0.09) and 0.89 (±0.054), respectively.
3.5. Effect of lubrication
Figures 8 and 9 show the sliding friction coefficient for a number of sig-nificant tests on both non-lubricated (Figure 8) and lubricated (Figure 9)interfaces. Each diagram of figure 8 and 9 refers to a different air temper-ature: (a) −10 ◦C, (b) 20 ◦C and (c) 50 ◦C, respectively, as well as to adifferent set of PTFE pads. Each series of data, instead, refer to a differentnormal load, resulting in 9.36, 18.7 and 28.1 Mpa contact pressure, respec-tively. In each diagram the experimental data have been gathered in fourgroups, based on the peak sliding velocity. Each group, therefore, corre-sponds to tests repeated under similar test conditions, after a certain num-ber of cycles. The displacement amplitude is generally different from onetest to another, within each group. The order of execution of the tests isgiven by the number beside each point.
By comparing Figures 8 and 9, it turns out that lubrication reduces fric-tion coefficient by about 5 times at −10 and 20 ◦C, and almost 8 timesat 50 ◦C. The sliding friction coefficient of lubricated steel–PTFE interfacesresults always below 4%, which is the limit value for sliding isolation devicesprescribed by the new Italian seismic code (Ordinanza 3274, 2003). The scat-ter in each group is practically negligible for non-lubricated interfaces, whileit is not for lubricated steel–PTFE interfaces. For these latter, the tendency isa progressive reduction of the friction coefficient while increasing the num-ber of cycles performed, due to the following reasons: (i) the introduction,in the sliding interfaces, of the grease contained inside the dimpled recessed,during the wear of the PTFE pads and (ii) the test sequence (see Table I),where tests wiith increasing displacement amplitude were carried out. Actu-ally, before the start of each test sequence, grease was spread over the PTFEpads, to fill the dimpled recesses, but a certain amount of grease was alsospread over the stainless steel sheets. When increasing displacement ampli-tude, it is reasonable to believe that more grease, from the stainless steelsheets, was introduced in the sliding interfaces.
The quite negligible scatter in the experimental results relevant to non-lubricated interfaces (see Figure 8) implies that the wear of PTFE (seebelow) do not affect significantly their frictional behavior. For the lubri-cated steel–PTFE interfaces, friction is much lower and the wear of PTFEis expected to be much less than for non-lubricated interfaces.
Figure 10 summarizes the results of all the tests on lubricated PTFE–steel interfaces. The sliding friction coefficient is reported as a function of(peak) velocity and contact pressure, for three different temperature values:(a) −10 ◦C, (b) 20 ◦C and (c) 50 ◦C, respectively. In the figure, experimental
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 89
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Figure 8. Effects of number of cycles on the sliding friction coefficient exhibited bynon-lubricated interfaces during tests at different air temperatures, namely: (a) −10 ◦C,(b) 20 ◦C and (c) 50 ◦C.
data and model predictions are compared. As can be seen, the frictioncoefficient of lubricated interfaces follows a trend similar to that describedfor non-lubricated interfaces. It tends to increase when increasing sliding
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Figure 9. Effects of number of cycles on the sliding friction coefficient exhibited bylubricated interfaces during tests at different air temperatures, namely: (a) −10 ◦C, (b)20 ◦C and (c) 50 ◦C.
velocity and to reduce when increasing air temperature and contact pres-sure. However a greater scatter can be noted, probably due to the testingsequence and the difficulty of getting uniform distribution of lubricatinggrease. The behavior of the friction coefficient at −10 ◦C is anomalous, asit increases while increasing contact pressure. Nevertheless, some interesting
Figure 10. Variation of the friction coefficient with sliding velocity, air temperatureand bearing pressure, for lubricated interfaces. Comparison between analytical lawsand experimental results. Air temperature equal to: (a) −10 ◦C, (b) 20 ◦C and(c) 50 ◦C.
92 M. DOLCE ET AL.
observation can be made by referring to the average values of the frictioncoefficient, over the three contact pressures. The friction coefficient underservice conditions (i.e. at very low sliding velocities) at 20 ◦C air tempera-ture is of the order of 1.5–2%. This is consistent with the values providedby AASHTO under the same conditions, ranging between 2 and 2.8%, forbearing pressures from 10 to 30 MPa. The sensitivity of the friction coeffi-cient to temperature variations resulting from the experimental data alsoconfirm the conservativeness of the property modification factors suggestedby AASHTO. They are λmax,t =1.5 at −10 ◦C and λmin,t =1 at 50 ◦C, whilethe experimental data under consideration provide values equal to 1.27(±0.09) and 0.59 (±0.07), respectively. CEN directly provides the maximumvalue of the friction coefficient to be used for verification of the bearingand the structure under service conditions. For expected extreme air tem-peratures lower than −5 ◦C, the above said design values ranges between3% (contact pressure ≥ 30 MPa) and 6% (contact pressure = 10 MPa), thusresulting about 2–3 times greater than the observed experimental values.Based on the present experimental study, therefore, the code recommenda-tions concerning the effects of extreme temperatures on the sliding frictioncoefficient of lubricated steel-PTFE interfaces appear to be enough or eventoo conservative. For lubricated interfaces, the friction coefficient is muchless sensitive to sliding velocity than for non-lubricated interfaces, as thevalues of the percent ratio θ = (µmax − µmin)/µmin is of the order of just25% at −10◦C and 20 ◦C, and 40% at 50 ◦C.
3.6. Effect of cycling
Cycling produces a double effect: (i) a reduction in the sliding frictioncoefficient, due to self heating of the steel–PTFE interfaces and (ii) wearof PTFE.
The first effect has been already discussed in 3.1. It has been foundthat higher sliding rates and pressures cause a larger decrease of the fric-tion coefficient. The decay, however, follows a negative exponential trend: itbecomes smaller and smaller while increasing the number of cycles. More-over, the reduction in the sliding friction coefficient is only temporary: itreturns to its original value when interrupting the cycling.
As said before (see Section 2.3), the PTFE pads were changed afterevery three series of tests, at the same air temperature. The thicknessesof the PTFE pads were then measured, on flat areas away from dimpledrecesses. As expected, the greatest wear of PTFE was observed at −10 ◦C,for interfaces with no lubrication. In this case, the thickness of the fourPTFE pads reduces by about 10%, passing from 5.4 to 4.9 mm, after hav-ing covered more than 30 m at different pressures and sliding velocities. Onthe contrary, the wear of lubricated PTFE was practically negligible.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 93
The wear is not a problem under seismic conditions, as an earthquakeproduces only a few cycles at the maximum displacement amplitudes. Itcould be important, instead, under service conditions. Actually, long-termtests are required by different codes and prescriptions, in order to appreci-ate the wear of PTFE due to slow movements resulting from both imposedthermal displacements and live loads. AASHTO, for instance, requires thatat least 50% of the usable PTFE thickness must remain after completion ofthe wear test, consisting in 1.6 Km at the design contact pressure, air tem-perature of 20±8 ◦C and sliding velocity not less 63.5 mm/min.
4. Modelling of Steel–PTFE Sliding Bearings
Two mathematical models of the frictional behavior of PTFE–steel inter-faces have been implemented.
According to Constantinou et al. (1990), the coefficient of friction atsliding velocity v, can be approximated by the following equation:
µ=µmax − (µmax −µmin) · e−α·v (2)
in which µmax is the coefficient of friction at high velocities, µmin is thecoefficient of friction at very low velocities and α is constant for a givenpressure, temperature and condition of interfaces. The frictional force isthen assumed equal to:
Fr =µ ·W ·Z (3)
where W is the normal load, Z is a dimensionless hysteretic quantity whichcan be calculated by solving the well-known differential equation proposedby (Wen, 1976) in random vibration studies of hysteretic systems.
The alternative proposed analytical law to describe the relationshipbetween sliding friction coefficient and velocity v is derived from (Changet al., 1990) and is given by:
{µ=a +b · ln(v) v >3 mm/sµ=a +b · ln(3) v ≤3 mm/s (4)
where a and b are constant for a given pressure, temperature and conditionof interfaces. The frictional force (Fr) is then expressed by Equation (3).
All the model parameters (i.e. µmax,µmin and α on one hand, a and b
on the other hand), have been analytically expressed as a function of P
(contact pressure) and T (air temperature), through a second-order poly-nomial model:
f (P,T )=λ1 +λ2 ·T +λ3 ·T 2 +λ4 ·P +λ5 ·P 2 (5)
94 M. DOLCE ET AL.
The coefficients λi have been obtained from a multivariate nonlinear regres-sion, using a statistical analysis package (SPSS, 1999).
The good fit of the regression, for both analytical laws, is apparentin Figure 5, which refers to non-lubricated interface. The proposed log-arithmic model, however, is more accurate in capturing the experimentalbehavior in the low velocity range than the Constantinou’s model, whichunderestimates the friction coefficient in that range.
For lubricated PTFE–steel interfaces (see Figure 10), the accuracy of themodel predictions is decidedly worse, due to the great scatter in the exper-imental results.
Tables II and III show the values of the model parameters for the ninecombinations of bearing pressure and air temperature considered duringthe tests on non-lubricated and lubricated interfaces, respectively. In thetables there are also compared the experimental and analytical maximumfriction forces at high peak velocities (160 mm/s, precisely). As can be seen,the error is at most equal to 5% for non-lubricated interfaces, while itranges between 1% and 43% for lubricated sliding interfaces. It should beconsidered, however, the different order of magnitude of the frictional forcefor non-lubricated and lubricated interfaces, whose average values are equalto about 2.5 and 0.45 kN, respectively. Thus, a 5% error implies an abso-lute error of 0.125 kN, in the first case, while a 43% error implies, in thesecond case, an absolute error of 0.193 kN. In any case, the maximum fric-tional force provided by the model can be reliably used in seismic isolationdesign.
Table II. Model parameters relevant to non-lubricated interfaces, for nine different combi-nations of bearing pressure and air temperature values.
Experimental test Constantiou’s model Logarithmic model
Comparison between experimental and analytical maximum frictional force at high peakvelocities (160 mm/s precisely)aPeak friction force at 160 mm/s maximum sliding velocity.bPercent error between experimental and numerical peak friction force.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 95
Table III. Model parameters relevant to lubricated steel–PTFE interfaces, for nine differentcombinations of bearing pressure and air temperature values.
Experimental test Constantiou’s model Logarithmic model
Comparison between experimental and analytical maximum frictional force at high peakvelocities (160 mm/s precisely)aPeak friction force at 160 mm/s maximum sliding velocity.bPercent error between experimental and numerical peak friction force.
The accuracy of the proposed model in capturing the actual fric-tional behaviour of steel-PTFE sliding bearings is confirmed by Fig-ures 11 and 12, which compare the experimental and numerical force–displacement loops of non-lubricated and lubricated interfaces, respec-tively. The experimental force-displacement relationships shown in Fig-ures 11 and 12 refer to the second cycle of the tests No. 13 and16 of Table I, at low and very high peak sliding velocities (i.e. about15 mm/s and about 316 mm/s, respectively). Both tests have been con-ducted with the same displacement amplitude (50 mm), contact pres-sure (18.72 MPa) and air temperature (20 ◦C). In the construction ofthe numerical relationships of Figures 11 and 12, reference was madeto the displacement-time histories, as drawn from the experimental out-put.
As far as non-lubricated interfaces are concerned, the accordancebetween experimental observations and model predictions is almost perfect,especially at low velocities. At high velocities, the numerical model is notable to capture the decay of the friction coefficient due to self-heating, asexpected. Larger differences between experimental and numerical results areobserved for lubricated interfaces, due to the big scatter in the experimen-tal outcomes and to the less sensitivity of the model to velocity variationduring the applied sinusoidal displacement.
As previously noted, the gap between minimum and maximum slidingfriction coefficient is significant for non-lubricated interfaces, while beingnegligible for lubricated steel–PTFE interfaces. Figures 11 and 12 clearlyprove this. As a consequence, it can be said that the behavior of lubricated
96 M. DOLCE ET AL.
Figure 11. Comparison between experimental and numerical force–displacement loopsof non-lubricated interfaces, at low and very high sliding velocities. Experimental testsconducted at 50 mm displacement amplitude, 18.72 MPa contact pressure and 20 ◦C airtemperature.
Figure 12. Comparison between experimental and numerical force–displacement loopsof lubricated steel–PTFE interfaces, at low and very high sliding velocities. Experimen-tal tests conducted at 50 mm displacement amplitude, 18.72 MPa contact pressure and20 ◦C air temperature.
steel–PTFE sliding bearings tends to be the same under seismic and serviceconditions, while considerable differences, in terms of maximum force andenergy loss, are found for non-lubricated steel–PTFE sliding bearings.
FRICTIONAL BEHAVIOR OF STEEL–PTFE INTERFACE 97
5. Conclusion
A comprehensive program of experimental tests on unfilled PTFE padssliding against polished stainless steel has been carried out. The effectson the sliding friction coefficient of (i) type of test, (ii) sliding velocity,(iii) contact pressure, (iv) air temperature, (v) conditi on of interfaces (i.e.lubricated or not) and (vi) number of cycles have been investigated. Thefollowing most important experimental findings have been obtained:
(1) The coefficient of friction increases rapidly with velocity, up to a cer-tain velocity value, beyond which it remains almost constant. Such valueis around 150 mm/s, regardless air temperature and bearing pressure. Themaximum velocities occurring in steel–PTFE sliding bearings under anearthquake are surely greater than 150 mm/s. Therefore, the design value ofthe frictional force in seismic applications can be assumed to be indepen-dent from frequency of loading and displacement amplitude.
(2) The sliding friction coefficient of steel–PTFE interfaces reduces whileincreasing pressure. The reduction rate, however, depends on both slid-ing velocity and air temperature. It increases while increasing velocity andwhile decreasing air temperature. By referring to 20 ◦C air temperature,18.7 MPa contact pressure and sliding velocities ≥150 mm/s, maximumvariations in the frictional force of steel–PTFE sliding bearings of the orderof 30% are expected for ±50% variations of the contact pressure, regardlessthe state of lubrication of the interfaces.
(3) The sliding friction coefficient decreases while increasing the air tem-perature. Its rate of reduction is greater when passing from low-to-mediumtemperatures, than when passing from medium-to-high temperatures. More-over, it depends on sliding velocity, while being practically independentfrom contact pressure. At sliding velocities of interest for seismic applica-tions, the reduction rate of the friction coefficient with temperature is ofthe order of 0.15–0.3%/◦C, for non-lubricated interfaces. As a consequence,upper and lower bound analysis is needed, in order to evaluate the maxi-mum forces on the structural elements and the maximum displacements inthe isolation system. To this end, reference can be made to the lambda-fac-tors (λmax,t and λmin,t ) provided by AASHTO, to estimate the values of thefriction coefficient at extreme design temperatures. Based on the experimen-tal results of the present study, the lambda-factors suggested by AASHTOlead to very accurate predictions for non-lubricated interfaces (differencesless than 10%), while they result too conservative for lubricated interfaces(overestimations up to 40%).
(4) The coefficient of friction tends to decrease during continuousloading cycles at high velocities, due to self-heating of the sliding inter-faces. The phenomenon is exhausted in a few cycles, due to the attain-ment of a new thermal equilibrium with the ambient. Based on the
98 M. DOLCE ET AL.
available experimental outcomes, the overall decay of friction with con-tinuous loading cycles is of the order of 25–30%, for non-lubricatedinterfaces.
(5) Lubrication considerably reduces (by 5–8 times, depending on tem-perature) the frictional resistance of steel-PTFE sliding interfaces and, asa consequence, the wear of PTFE. In addition, the use of silicone greasestrongly diminishes the gap between maximum and minimum frictioncoefficients and, then, the differences in the structural response betweenseismic and service conditions. On the other hand, the use of siliconegrease increases the sensitivity to temperature variations of the mechanicalbehaviour of steel–PTFE sliding bearings.
A mathematical model of the frictional behavior of steel–PTFE slidinginterfaces has been presented, which takes into account the dependence ofthe frictional force on sliding velocity, contact pressure and air tempera-ture.
The proposed model describes the relationship between friction coeffi-cient and sliding velocity through a logarithmic analytical law. The modelis characterised by two parameters, which are analytically expressed as afunction of contact pressure and air temperature, through a second-orderpolynomial equation.
The accuracy of the proposed model in capturing the actual frictionalbehaviour of steel–PTFE sliding bearings has been verified by comparingthe experimental and numerical force–displacement loops of non-lubricatedand lubricated interfaces. It has been proved that the maximum frictionalforce provided by the model can be reliably used in the design of seismi-cally isolated structures.
Acknowledgements
The authors are indebted with Ing. Roberto Marnetto (TIS SpA), andMr Domenico Nigro (University of Bailicata) which have cooperated in thesetting up of the testing apparatus. This work has been partially funded byMIUR, COFIN 2002.
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