: 1 st Euro-Mediterranean Conference 23-25 Apr 2013 on Structural Dynamics and Vibroacoustics Marrakech (Morocco) ABSTRACT DYNAMIC FRICTION COMPACT MODEL : A NEW MULTICONTACT TRIBOMETER J.L.DION, G.CHEVALLIER, O.PENAS, F.RENAUD 1Lab or Company Name LISMMA- EA 2336 SUPMECA - 3 rue Fernand Hainaut 93407 Saint Ouen Cedex France jean-luc.dion@supmeca.fr This paper presents an original friction measurement setup. It is designed to uncouple normal and tangential load. Friction measures acquired with this setup present a high signal to noise ratio. This friction experimental device allows characterizing various types of surfaces and several levels of excitation from static strain to dynamical motion including micro-sliding and macrosliding. A measurement example is presented for a contact pair of Aluminum alloy starting from sticking limit until complete sliding. Finally, in order to use the results in vibration reduced models, a method is proposed to identify the compact Lugre Model from these measurements.
1 DESCRIPTION Many previous works use or have developed tribometers ([1-11], [16-21]) The proposed test bench allow to uncouple normal and tangential loads over a wide frequency bandwidth to ensure the good quality of measurements and test conditions, as previously exposed. In order to verify this assumption and to identify state and rate models, normal force, tangential force, relative displacement and sliding velocity have to be measured over a large frequency range and with a great accuracy. Our tribometer has been so mounted on a MTS Elastomer Test System 830 which allows to obtain at 200 Hz a [1-100] µm displaceme ent range inducing a [1.2-120] mm/s velocity range. To decouple normal and tangential load, the test setup is composed of three orthogonal symmetry-planes with four contact areas (Figure 1 and Figure 3). Each symmetry-plane allows an equal repartition of normal forces (planes P1 & P2) and tangential forces (plane P3). The complete experimental set, composed of samples in the tribometer, is iso-static. The base sample (Figure 1) is clamped on the reference frame of the hydraulic machine but the mobile sample is free in rotation around the jack displacement axis and avoids hyperstatism in the mechanism. For the same reason, the normal force (N) is performed with a flexible screw. The axis of this screw is placed along the intersection of planes P1 and P2. Moreover, the two application points of the normal force applied by the screw are symmetric on both sides of P3. These technical choices allow to assume a satisfying symmetry for three orthogonal planes, both for geometric properties of the mechanical setup and for load distributions. Figure 1: Principle of contact areas and normal and tangential forces The three orthogonal symmetry-planes (P1, P2 and P3) allow decoupling between normal and tangential forces and an equal repartition of these forces on each sample. 2
23-25 Apr 2013,, Marrakech (Morocco) During the test, with tangential motion, motion static normal load is assumed to remain static. However the normal load is always measured and controlled with high frequency sampling during the test. This assumption is often not verified on other tribometers. A particular attention has been paid in the the design of this tribometer in order to avoid coupling between normal and tangential load. For all the tests, hydraulic jack movements are displacement controlled with the feed-back feed signal of the internal displacement transducer (LVDT). Measurements are performed with 3 force sensors (Fn, Ft, Ft2), 1 LVDT displacement sensor (X), 3 Foucault displacement sensors (xm, xh, xb) and 2 accelerometers (Ae, Af). Most of them are used in order to verify assumptions, ions, only 3 sensors are necessary for dynamic friction measurement : 2 force sensors (Ft, Fn) n) and 1 displacement LVDT (X). Figure 2:: Schema and partial picture of the tribometer. tribomet IDENTIFIC 3 COMPACT MODEL SELECTION AND PARAMETRIC IDENTIFICATION Many compact models have already been developed in previous works ([12]]-[15], [22-29]). The LuGre model [14] can be considered as an evolution of Dahl s model with a velocity dependant friction factor introduced by the g function, often chosen ch en as a Gaussian function. function The LuGre model was completed in 2002 [12] and it includes elastoplastic behavior that occurs before the slipping limit has been reached. Ft = ( K 0 z + C0 zɺ + C1 xɺ ) Fn xɺ dz = xɺ K 0 z dt g ( xɺ ) g ( xɺ ) = µ d + ( µ s µ d ) e 3 (1) xɺ Vs α
The proposed identification method is robust and has been applied for a very large number of tests with several frequencies and normal loads. The quality of fitting between simulation and measurements in Figure 3 is similar for most of the tests; some are better while only a few (less than 5%) are worse. Figure 3: Comparison between measurement and simulation obtained with the proposed identification method 2 CONCLUSION This work was performed in the field of structural vibrations. In a complex mechanism, the level of vibration strongly depends on the dissipation in the connected parts. This work presents a new test bench designed for improving the accuracy of measurements of non linear dissipative behaviors of frictional interfaces. This test bench is used for dynamic friction studies. Magnitudes of displacement have been tested from 10-5 m to 10-2 m while those of velocity have been studied from 10-7 m/s to 10 m/s. The tribometer design allows a very good independence between normal and tangential forces. Measurement techniques and signal processing methods highlight excellent accuracy with both direct measurements and parametric identification. As an illustration and because it is very well-formulated for vibrations problems, the LuGre Model has been identified from experimental results. An accurate method for parametric identification has been performed and a rheological description of the LuGre model has been presented. The prospects for improvement of this test means are to enable the measurements of the dissipative behavior on the scale of roughness. Thus the next test bench should make it possible to obtain measurements of displacements under 10-7 m. 4
REFERENCES [1] Chevallier G., «Etude des vibrations de broutement provoquées par le frottement sec - application aux systèmes d embrayage», UPMC, Paris, 2005. [2] Camara M., Robbe-Valloire F., Gras R., Chen Y.-M. "Development of a pin-on disc type tribotester in order to study the influence of dynamic load on the tribological behaviour" Presses polytechniques et universitaires romandes, ISBN 978-2-88074-775-6, p. 65-74, 2008 [3] De Moerlooze K., Al-Bender F." On the relationship between normal load and friction force in pre-sliding frictional contacts. Part 2: Experimental investigation" Wear Vol. 269,p.183 189, 2010 [4] Mulvihill D.M., Kartala M.E., Olverb A.V, Nowella D., Hills D.A. "Investigation of non- Coulomb friction behaviour in reciprocating sliding", Wear, Vol. 271 p.802 816, 2011 [5] Eriten M., Lee C.-H., Polycarpou A. "Measurements of tangential stiffness and damping of mechanical joints: Direct versus indirect contact resonance methods" Tribology International, Vol.50, p. 35 44, 2012. [6] Guibert M., Nauleau B. Kapsa P. Rigaud E. "Design and manufacturing of a recipocating linear tribometer", Tribologie et couplages multiphysiques, Presses polytechniques et universitaires romandes, ISBN 978-2-88074-775-6, p. 55-64, 2008 [7] Coulomb C. A., «Théorie des machines simples», in Mémoires de Mathématique et de Physique de l Académie des Sciences, 1785, p. 161-335. [8] Makris N. and Chang S.-P. "Effect of vscous, viscoplastic and friction damping on the response of seismic isolated structures" ISET Journal of Earthquake Technology, Paper N 379, Vol.35, Issue N 4,pp. 113-141, 1998 [9] Adams V. and Askenazi A. "Building Better Products with Finite Element Analysis" OnWord Press, Santa Fe, N.M., 1999. [10] Cremer L. and Heckl M., "Structure-Borne Sound", Springer-Verlag, New York,1988. [11] Nouira H., Foltete E., Aitbrik B., Hirsinger L., et Ballandras S., «Experimental characterization and modeling of microsliding on a small cantilever quartz beam», Journal of Sound and Vibration, vol. 317, no. 1-2, p. 30-49, 2008. [12] Almajid A., «Harmonic response of a structure mounted on an isolator modelled with a hysteretic operator: experiments and prediction», Journal of Sound and Vibration, vol. 277, no. 1-2, p. 391-403, 2004. [13] Awrejcewicz J. et Lamarque C. H., Bifurcation and Chaos in Non-smooth Mechanical Systems. Singapore: World Scientific Publishing, J. 2003. [14] Canudas de Wit C., Olsson H., Astrom K. J., et Lischinsky P., «A new model for control of systems with friction», IEEE Transactions on Automatic Control, vol. 40, no. 3, p. 419-425, 1995. [15] Dahl P., «A solid Friction Model», The Aerospace Corporation, El Segundo, CA, TOR- 0158H3107 18I-1, 1968. [16] Baumerger T., Bureau L., Busson M., Falcon E., et Perrin B., «An inertial tribometer for measuring microslip dissipation at a solid solid multicontact interface», REVIEW OF SCIENTIFIC INSTRUMENTS, vol. 69, no. 6, p. 2416-2420, 1998. 5
[17] Lampaert V., Al-Bender F., et Swevers J., «Experimental Characterization of Dry Friction at Low Velocities on a Developed Tribometer Setup for Macroscopic Measurements», Tribology Letters, vol. 16, no. 1/2, p. 95-105, 2004. [18] Huang X. and Neu R.W., «High-load fretting of Ti 6Al 4V interfaces in point contact», Wear, vol. 265, no. 7 8, p 971-978, 2008. [19] ] Fouvry S., Duó P. and Perruchaut P. «A quantitative approach of Ti 6Al 4V fretting damage: friction, wear and crack nucleation», Wear, vol. 257, no 9 10, p 916-929, 2004. [20] Guicciardi S., «On data dispersion in pin-on-disk wear tests», Wear, vol. 252, no. 11-12, p. 1001-1006, 2002. [21] Quinn D. D., «Modal analysis of jointed structures», presented at the IDETC, Washington DC, 2011. [22] Al-Bender F., Lampaert V. and Swevers J. "The Generalized Maxwell-Slip Model: A Novel Model for Friction Simulation and Compensation" IEEE Transactions On Automatic Control, Vol. 50, N 11, p.1883-1887, 2005 [23] Stribeck R., «Die Wesentlichen Eigenschaften der Gleit - und Rollenlager - the key qualities of sliding and roller bearings», Zeitschrift des Vereines Seutscher Ingenieure, vol. 46, no. 38-39, p. 1342-1348, 1902. [24] Segalman D.J. "A Four-Parameter Iwan Model for Lap-Type Joints" Journal of Applied Mechanics, Vol. 72, Issue 5, p.752-760, 2005. [25] Lampaert V., Swevers J. and Al-Bender F. "Modification of the Leuven Integrated Friction Model Structure", IEEE Transactions On Automatic Control, Vol. 47, N 4, p. 683-687, 2002 [26] Szolwinski M., «Observation, analysis and prediction of fretting fatigue in 2024-T351 aluminum alloy», Wear, vol. 221, no. 1, p. 24-36, 1998. [27] Mo J. L., Zhu M. H., Zheng J. F., Luo J., and Zhou Z. R., «Study on rotational fretting wear of 7075 aluminum alloy», Tribology International, vol. 43, no. 5-6, p. 912-917, 2010. [28] Liu H., «Tensile properties and fracture locations of friction-stir-welded joints of 2017- T351 aluminum alloy», Journal of Materials Processing Technology, vol. 142, no. 3, p. 692-696, 2003. [29] Bowden F. et Tabor D., The friction and lubrication of solids. Oxford: Clarendon Press, 1950.N. Name, N. Name, and N. Name. Book Title. Publisher, City, 2013. 6