Csatár, Attila

Safranyik, Ferenc

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AbstractThe phenomenon of friction reduces the efficiency of almost allmachines in practice. For reduce the deficits we have tounderstand this phenomenon and we have to take it in all casesinto consideration during design. Nevertheless in certain casesthe describing of a friction process is very difficult; because thisdepends on a lot of parameters. In case of polymers, granularmaterials or in geology the rate- and state dependent friction havegreat importance. In this paper velocity- and time dependentfriction of polyamide and steel is examined with the help of adirect shear apparatus, which was developed in our earlier work.Based on the results of experimental measurements the previouslydeveloped apparatus is suitable for examine time dependentproperties of friction.Keywordsfriction, time-dependence, velocity-dependence1. IntroductionThe friction process was examined first almost three centuriesago by Coulomb [5] and it was discovered that the kinetic frictiondoes not depend on the shear velocity. Later with more preciseexperiments showed that this phenomenon depends on a lot ofparameters, such as materials, roughness, temperature or the shearvelocity. Due to the diverse parameters the description of afriction process is very difficult in certain cases. In geology,mining- and earthquake science, in case of polymers, granularmaterials or other special materials the time- and velocity-dependent friction (creep and relaxation) have great importanceand only few researchers investigate the thermodynamic aspectsof this time dependence of friction [6, 7, 8]. The aim of our workis to examine the velocity dependent friction of polyamide andsteel and the revise of the previously by our developed directshear testing apparatus.1.1 Friction testThe knowledge on the shear strength is very important indescription of a friction process. This parameter means therelationship between the displacement and the shear force and alot of parameters have influence on this [1]. The shear strengthcan be evaluated by using direct shear test; in course of this thesurfaces are pressed together with constant normal loadmeanwhile moving on each other. During the shear process, theshear force is measured as function of displacement. The materialproperties, the roughness and the shear velocity have greatinfluence on shear strength [1].During the direct shear test of two smooth surfaces (underconstant normal load and constant shear velocity) the shearstrength increases to an initial peak, which is followed by slowlydisplacement weakening and then stabilization at a residual shearstrength, which does not change or increases very slowly withadditional displacement [1].Based on shear tests with different normal loads, the shearstrength is in linear correlation with normal strength. The slopeof this line is the friction coefficient concerning to the materials,the designate constant of this line is the cohesion between thesurfaces. The shear strength is based on the Mohr-Coulombequation [5]:where c is the cohesion,   is the friction angle between thesurfaces.The residual strength is [5]:where   is the residual friction angle between the surfaces.1.2 Time- and velocity-dependent experimentsThe time- and velocity-dependent friction have great importancein geology: faults may undergo decelerating postseismic slip(afterslip), long term stable slip (fault creep) in the absence ofearthquake instability, and perhaps slow postseismic slip [2]. Forthis reason Dietrich et al. made laboratory shear experiments withclean surfaces of granite [3, 4] and with a layer of simulated faultgouge consisting of crushed and sieved granite [2]. Theseexperiments were made with different shear parameters (normalload, shear velocity). The sample assembly consists of a threeblocks, sandwich type direct shear configuration (Fig. 1.).Three different types of tests were made: constant velocity,multiple velocity and time dependence shear tests. The constantvelocity tests were made at 2.5 µm/s (Fig. 2/a). In the multiply-20HUNGARIAN AGRICULTURAL ENGINEERING N° 26/2014 20-24Published online: http://hae-journals.org/HU ISSN 0864-7410 (Print) / HU ISSN 2415-9751(Online)DOI: 10.17676/HAE.2014.26.20EXAMINING THE VELOCITY- AND TIME-DEPENDENT FRICTION INCASE OF STEEL AND POLYAMIDEAuthor(s):A. Csatár1 – F. Safranyik2Affiliation:1Scientific Deputy General Director, Hungarian Institute of Agricultural Engineering2Szent István University, Faculty of Mechanical Engineering, Department of Mechanics and Technical DrawingEmail address:csatar.attila@gek.szie.hu, safranyik.ferenc@hallgato.szie.huPERIODICAL OF THE COMITTEE OFAGRICULTURAL AND BIOSYSTEMENGINEERING OF THE HUNGARIANACADEMY OF SCIENCES and SZENT ISTVÁN UNIVERSITYFaculty of Mechanical Engineering12velocity tests the shear velocity was constant for apredeterminated displacement, then suddenly changed by a factorof 10, held constant for another displacement then changed againand so on (Fig. 2/b). The third group of shear test was the time-dependence tests, in which constant velocity shear wasinterrupted at a specified displacement where the controldisplacement is held at zero for a specified time interval (Fig. 2/c)[2].Figure 1. The sample assembly by Dietrich [2]The aim of the constant velocity tests were to examine theoverall form of stress-displacement curves (Fig. 2/d) to permitreasonably direct comparison to be made for the control ofstrength by the fault parameters. Based on these curves the shearstrength increases to an initial peak, which is followed by a slowdisplacement weakening and then stabilization at residual shearstrength (Fig. 2/d). If the shear stress cycling to zero afterreaching residual strength, acts to restore the peak in the stress-displacement curves. This cycling increases the totaldisplacement and also the peak and residual strength [2].Figure 2. a) Constant velocity test; b) Multiply velocity-test;c) Time dependence test; d) Shear diagram with constantvelocity and normal stress [2]The purpose of the multiply-velocity tests was to look forvariations of strength as a function of velocity. A step increase ofshear velocity results an immediate jump in frictional coefficientfollowed by displacement dependent decay and stabilization at anew steady-state friction. The reverse is seen if the shear speedis decreased (Fig. 3.) [3].Dietrich and Kilgore [3] made a shear rate- and state-dependentconstitutive formulation for fault tests. This formulation providesa descriptive framework for the interpretation of the transientshearing phenomenon. The coefficient of friction can berepresented [3]:where   and   are shear and normal stress V is a shear speed andis a state variable. Parameters , A and B are experimentallydetermined constants and V* and   are normalizing constants [3]. 1.3 The developed shear testing apparatusThe design of our test apparatus was made on the basis ofDietrich’s vertical shear tester [2]. In case of Dietrich’sarrangement the displacement was vertical and the normal forcewas horizontal, while in our case the normal force is provided byan INSTRON 5581 type universal material testing machine, so itshould be vertical thus the displacement must be horizontal. Theshear force was measured by a load cell which is at the holdingpoint of the fixed part; the displacement was measured by aninductive displacement transducer at the moving part. Thedisplacement provided by a stepper motor (Fig. 4.).21Figure 3. Effect of steps in shear speed on a friction coefficient, the case of velocity weakening [3]3On Fig. 4 the finished shear apparatus can be seen: 1 – steppermotor; 2 – screw shaft and cased coupling; 3 – displacementtransducer; 4 – nut; 5 – fixed part; 6 – moving part; 7 – load cell;8 – INSTRON 5581. The normal load was provided by theINSTRON 5581 type universal material testing machine the loadwas transferred trough a steel ball that ensures the punctual loadto the fixed part.The chosen motor is a three phase stepper motor that divides afull rotation into a number of equal steps; therefore in order toachieve the minimum speed a XINJE DP-7022 digital stepperdrive was used. With its microstep function no more than 65535step/rotation can be set up which ensures the low and exactangular velocity of the stepper motor. Microstepping is a way ofmoving a stepper smoothly. The measurement system of theappliance is a separate module. The displacement is measured byan HBM WETA 1/10 inductive economic displacementtransducer, the shear force by an HBM U9B 5 kN forcetransducer. The Spider 8 and the Catman 4.5 software carry outthe data acquisition. [9]2. Experimental measurements and resultsExperimental measurements were carried out with polyamide andsteel probes. The usual experimental protocol for evaluating sliprate and state dependence of friction of changing the shearvelocity in a stepwise manner under of constant normal stress.Normal stress was held constant during the measurements whichwere ensured by the force regulated INSTRON 5581 universalmaterial testing machine. Multiple velocity tests were carried outwith constant shear velocity for a predetermined displacement,then suddenly changed by a factor of 10, then held constant foranother displacement and changed back to the first velocity. Thetests were carried out with two different speed levels, 2 and 4µm/s, for both materials. Additionally two different normal stresslevels were investigated, 20 and 40 kPa. During the tests the shearforce and the displacement were measured and the shear diagramswere determined (Fig. 5.).The purpose of these multiple-velocity tests was to look thetime dependent friction coefficient as seen in the earlier rockfriction experiments of Dietrich [2, 4, 6]. In these earlier workstwo different velocity effects was observed, the step increase ofshear velocity results in an immediate jump in frictionalcoefficient followed by displacement dependent decay andstabilization at a new steady-state friction. The reverse is seen ifthe shear speed is decreased. This friction coefficient jump on thehigher speed level and the decrease on lower speed level can beseen on the shear diagrams (Fig. 5.).Step changes of velocity results residual and transient changesin friction coefficient. Firstly at constant sliding velocity hasproceeded for a sufficient distance for µ to have stabilized at aresidual value (µ1) then due to the suddenly increase of velocityproduces an immediate increase in friction coefficient then thisfollowed by a decrease (µ2) to a new residual value. This newresidual value is generally less than the residual coefficient on theprevious slower velocity phase. After predetermined slidingdisplacement the shear velocity abruptly decrease to thepreviously lower level results a positive jump in the frictioncoefficient to a new residual value (µ3), which is greater than theresidual coefficient at the first phase of the test with the samesliding velocity.22Figure 4. The test assembly and the finished apparatus23Figure 5. Displacement in function of timeFigure 6. Friction coefficient versus displacementBased on the different measurements determinable that the µ1,µ2, µ3 values depend on the normal stress and the material. Incase of rigid materials (steel) the residual friction coefficientdecrease and increase are greater than a less rigid material(polyamide). Based on these observation verifiable that our shearapparatus (which based on Dietrich’s work) is suitable forexamine the time- and velocity-dependence of friction.3. SummaryWe have developed a simple experimental device for testing time-and velocity dependent properties of friction. The firstmeasurements were performed with poliamid and steel. Theyshow velocity weakening and stick-slip phenomena at the highervelocity level for both materials.  Therefore we havedemonstrated, that the apparatus is able to reproduce severalimportant time dependent friction phenomena and therefore it issuitable for experimental investigations. We have alsoinvestigated effects related to shear strhength.4. AcknowledgmentThis paper was supported by the János Bolyai ResearchScholarschip of the Hungarian Academy of Sciences.References[1] Asszonyi, Cs., Kertész, P., Richter, R.: A kőzetmechanikaanyagszerkezeti és reológiai alapjai, Veszprémi AkadémiaiBizottság, Veszprém, 1980, pp. 446.[2] Dietrich, J. H.: Constitutive properties of faults withsimulated gouge, Geophysical Monograph Series, Vol. 24, 1981,p. 103-120.[3] Dietrich, J. H., Kilgore, B. D.: Direct observation offrictional contacts: New insights for state-dependent properties,Pure and Applied Geophysics PAGEOPH, Vol. 143, 1994, p. 283-302.[4] Dietrich, J. H.: Modeling of Rock Friction I.: ExperimentalResults and Constitutive Equations, Journal of GeophysicalResearch, Vol. 84, 1979, p. 2161-2168.[5] Dowson, D.: History of tribology, Longman, New York, 1979.[6] Ruina, A. L.: Slip Instability and State Variable FrictionLaws, Journal of Geophysical Research, Vol. 88, 1983, p. 10359-10370.[7] N. Mitsui and P. Ván: Thermodynamic aspects of rockfriction, Acta Geodaetica et Geophysica, Vol. 49, 2014, p.135-146, (arXiv:1312.4930 [physics.geo-ph])[8] Ván P.: A képlékenység termodinamikája. In: Fülöp T.(szerk.) Idő és térderiváltak anyagtörvényekben. Mérnök geo -lógia-Kőzetmechanika Kiskönyvtár 10, Műegyetemi Kiadó,Budapest, 2010, pp. 15-50.[9] A. Csatár; F. Safranyik; G. Bércesi: A NEW direct sheartesting apparatus for the examination of the velocity- and time-dependent friction, Hungarian Agricultural Engineering 25;  p.54-58; (ISSN 0864-7410)24Figure 7. The changes of residual strengths in case of different normal stress

Examining The Velocity- and Time-Dependent Friction in Case of Steel and Polyamide

A. Csatár

F. Safranyik

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Hungarian Agricultural Engineering

English