Friction modeling for dynamic system simulation

[+] Author and Article Information
EJ Berger

CAE Laboratory, Department of Mechanical, Industrial, and Nuclear Engineering, University of Cincinnati, PO Box 210072, Cincinnati, OH 45221-0072ed.berger@uc.edu

Appl. Mech. Rev 55(6), 535-577 (Oct 16, 2002) (43 pages) doi:10.1115/1.1501080 History: Online October 16, 2002
Copyright © 2002 by ASME
Topics: Friction , Force
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Coulomb CA (1785), Theorie des machines simples, Memoirs de Mathematique et de Physique de l’Academie Royale, 161–342.
Kalker JJ (1990), Three-Dimensional Elastic Bodies in Rolling Contact. Dordrecht, Kluwer Academic Publishers, Boston.
Ibrahim  RA (1994), Friction-induced vibration, chatter, squeal, and chaos: Part I-Mechanics of contact and friction, Appl. Mech. Rev. 47(7), 209–226.
Ibrahim  RA (1994), Friction-induced vibration, chatter, squeal, and chaos: Part II-Dynamics and modeling, Appl. Mech. Rev. 47(7), 227–253.
Ferri  AA (1994), Friction damping and isolation systems, ASME Special 50th Anniversary Design Issue 117, 196–206.
Feeny  B, Guran  A, Hinrichs  N, and Popp  K (1998), A historical review on dry friction and stick-slip phenomena, Appl. Mech. Rev. 51, 321–341.
Back N, Burdekin M, and Cowley, A (1973), Review of the research on fixed and sliding joints, Proc of 13th Int Machine Tool Design and Research Conf, SA Tobias and F Koenigsberger (eds), MacMillan, London, 87–97.
Beards  CF (1983), The damping of structural vibration by controlled interfacial slip in joints, ASME J. Vib., Acoust., Stress, Reliab. Des. 105, 369–373.
Goodman LE (1959), A review of progress in analysis of interfacial slip damping, Structural Damping, JE Ruzicka (ed), ASME, 36–48.
Ungar  E (1973), The status of engineering knowledge concerning the damping of built-up structures, J. Sound Vib. 26(1), 141–154.
Sampson  JB, Morgan  F, Reed  DW, and Muskat  M (1943), Friction behavior during the slip portion of the stick-slip process, Journal of Applied Physics 14(12), 689–700.
Rabinowicz E (1958), The intrinsic variables affecting the stick-slip process, Proc of Physical Society of London, 471 , 668–675.
Bell R and Burdekin M (1969–1970), A study of the stick-slip motion of machine tool feed drives, Proc. of Inst. of Mech. Eng.184 (1), 543–557.
Hess  DP and Soom  A (1990), Friction at lubricated line contact operating at oscillating sliding velocities, ASME J. Tribol. 112, 147–152.
Hunt  JB, Torbe  I, and Spencer  GC (1965), The phase-plane analysis of sliding motion, Wear 8, 455–465.
Pavelescu  D and Tudor  A (1987), The sliding friction coefficient-its evolution and usefulness, Wear 120, 321–336.
Lin  Y-Q and Wang  Y-H (1991), Stick-slip vibration in drill strings, ASME J. Eng. Ind. 113, 38–43.
Popp K (1992), Some model problems showing stick-slip motion and chaos, Friction-Induced Vibration, Chatter, Squeal, and Chaos, ASME, DE-Vol 49, 1–12.
Bengisu MT and Akay A (1992), Stability of friction-induced vibrations in multi-degree-of-freedom systems, Friction-Induced Vibration, Chatter, Squeal, and Chaos, ASME, DE-Vol 49, 57–64.
Bengisu MT and Akay A (1992), Interaction and stability of friction and vibrations, IL Singer and HM Pollock (eds), Fundamentals of Friction: Macroscopic and Microscopic Processes, Kluwer Academic Pub, 553–566.
de Velde  FV and Baets  PD (1996), Mathematical approach of the influencing factors on stick-slip induced by decelerative motion, Wear 201, 80–93.
Dupont  PE (1994), Avoiding stick-slip through pd control, IEEE Trans. Autom. Control 39(5), 1094–1097.
Lim  YF and Chen  K (1998), Dynamics of dry friction: A numerical investigation, Phys. Rev. E 58(5), 5637–5642.
Rice  JR and Ruina  AL (1983), Stability of steady frictional slipping, ASME J. Appl. Mech. 50, 343–349.
Gu  J-C, Rice  JR, Ruina  AL, and Tse  ST (1984), Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction, J. Mech. Phys. Solids 32(3), 167–196.
Tolstoi  DM (1967), Significance of the normal degree of freedom and natural normal vibrations in contact friction, Wear 10, 199–213.
Greenwood  JA and Williamson  J (1966), Contact of nominally flat surfaces, Proc. R. Soc. London, Ser. A A295, 300–319.
Nayak  PR (1972), Contact vibrations, J. Sound Vib. 22(3), 297–322.
Gray  GG, and Johnson  KL (1972), The dynamic response of elastic bodies in rolling contact to random roughness of their surfaces, J. Sound Vib. 22(3), 323–342.
Godfrey  D (1967), Vibration reduces metal-to-metal contact and causes an apparent reduction in friction, ASLE Trans. 10, 183–192.
Antoniou  SS, Cameron  A, and Gentle  CR (1976), The friction-speed relation from stick-slip data, Wear 36, 235–254.
Sakamoto  T (1987), Normal displacement and dynamic friction characteristics in a stick-slip process, Tribol. Int. 20(1), 25–31.
Bo  LC and Pavelescu  D (1982), The friction-speed relation and its influence on the critical velocity of stick-slip motion, Wear 82, 277–289.
D’Souza  AF and Dweib  AH (1990), Self-excited vibrations induced by dry friction, Part 1: Experimental study, J. Sound Vib. 137(2), 163–175.
D’Souza  AF and Dweib  AH (1990), Self-excited vibrations induced by dry friction, Part 2: Stability and limit-cycle analysis, J. Sound Vib. 137(2), 177–190.
Soom  A and Kim  C (1983), Interaction between dynamic normal and frictional forces during unlubricated sliding, J. Lubr. Technol. 105, 221–229.
Soom  A and Kim  C (1983), Roughness-induced dynamic loading at dry and boundary lubricated sliding contacts, J. Lubr. Technol. 105, 514–517.
Anand  A and Soom  A (1984), Roughness-induced transient loading at a sliding contact during start-up, ASME J. Tribol. 106, 49–53.
Soom  A and Chen  JW (1986), Simulation of random surface roughness-induced contact vibrations at hertzian contacts during steady sliding, ASME J. Tribol. 108, 123–127.
Polycarpou  AA and Soom  A (1995), Boundary and mixed friction in the presence of dynamic normal loads: Part I-System model, ASME J. Tribol. 117, 255–260.
Polycarpou  AA and Soom  A (1995), Boundary and mixed friction in the presence of dynamic normal loads: Part II-Friction transients, ASME J. Tribol. 117, 261–266.
Polycarpou  AA and Soom  A (1995), Two-dimensional models of boundary and mixed friction at a line contact, ASME J. Tribol. 117, 178–184.
Rice SL, Moslehy FA, and Elmi S (1993), Tribodynamic modeling, 19th Leeds-Lyon Symp-Thin Films in Tribology, D Dowson et al. (eds), Elsevier, New York, 641–648.
Streator  JL and Bogy  DB (1992), Accounting for transducer dynamics in the measurement of friction, ASME J. Tribol. 114, 86–94.
Oden  JT and Martins  JAC (1985), Models and computational methods for dynamic friction phenomena, Comput. Methods Appl. Mech. Eng. 52, 527–634.
Hess  DP and Soom  A (1992), Normal and angular motions at rough planar contacts during sliding with friction, ASME J. Tribol. 114, 567–578.
Jarvis  RP and Mills  B (1963–64), Vibrations induced by dry friction, Proc. of Inst. of Mech. Eng. 178(32), 847–866.
Earles  SWE and Lee  CK (1976), Instabilities arising from the frictional interaction of a pin-disk system resulting in noise generation, ASME J. Eng. Ind. 98(1), 81–86.
Earles SWE and Soar GB (1971), Squeal noise in disk brakes, Proc of Inst of Mech Eng, Vibration and Noise in Motor Vehicles, 61–69.
Earles  SWE and Badi  MNM (1984), Oscillatory instabilities generated in a double-pin and disc undamped system: A mechanism of disc-brake squeal, Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci. 198C, 43–50.
Swayze JL and Akay A (1992), Effects of systems dynamics on friction-induced oscillations, Friction-Induced Vibration, Chatter, Squeal, and Chaos, ASME, DE-Vol 49, 49–55.
Martins  JAC, Oden  JT, and Simoes  FMF (1990), A study of static and kinetic friction, Int. J. Eng. Sci. 28, 29–92.
Tworzydlo  WW, Becker  EB, and Oden  JT (1994), Numerical modeling of friction-induced vibrations and dynamic instabilities, Appl. Mech. Rev. 47(7), 255–274.
Tworzydlo  WW and Becker  E (1991), Influence of forced vibrations on the static coefficient of friction-numerical analysis, Wear 43, 175–196.
Madakson  PB (1983), The frictional behavior of materials, Wear 87, 191–206.
Froslie LE, Milek T, and Smith EW (1973), Automatic transmission friction elements, Design Practices-Passenger Car Automatic Transmissions, Soc of Autom Eng, 535–552.
Anderson  JR, and Ferri  AA (1990), Behavior of a single-degree-of-freedom system with a generalized friction law, J. Sound Vib. 140(2), 287–304.
Menq  C-H, Griffin  JH, and Bielak  J (1986), The influence of microslip on vibratory response, part ii: A comparison with experimental results, J. Sound Vib. 107(2), 295–307.
Dupont  PE, and Bapna  D (1994), Stability of sliding frictional surfaces with varying normal forces, ASME J. Vibr. Acoust. 116, 237–242.
Berger  EJ, Krousgrill  CM, and Sadeghi  F (1997), Stability of sliding in a system excited by a rough moving surface, ASME J. Tribol. 119(4), 672–680.
den Hartog  JP (1931), Forced vibrations with combined coulomb and viscous damping, ASME J. Appl. Mech. APM-53-9, 107–115.
Blok  H (1940), Fundamental aspects of boundary friction, J. Soc. Autom. Eng. 46, 275–279.
Derjaguin BV, Push VE, and Tolstoi DM (1957), A theory of stick-slip sliding in solids, Proc Conf on Lubrication and Wear, 257–268.
Brockley  CA, Cameron  R, and Potter  AF (1967), Friction-induced vibration, J. Lubr. Technol. 89, 101–108.
Brockley  CA and Ko  PL (1970), Quasi-harmonic friction-induced vibration, J. Lubr. Technol. 92, 550–556.
Pfeiffer F and Glocker C (1996), Multibody Dynamics with Unilateral Contacts, Wiley Series in Nonlinear Science, John Wiley and Sons, New York.
Guran A, Pfeiffer F, and Popp K (1996), Dynamics with Friction-Modeling, Analysis, and Experiment, Part I, World Sc, Singapore.
Popp  K (1995), Dynamical behaviour of a friction oscillator with simultaneous self and external excitation, Sadhana: Proc., Indian Acad. Sci. 20(2–4), 627–654.
Budd  C and Dux  F (1994), Chattering and related behavior in impact oscillators, Philos. Trans. R. Soc. London, Ser. A A347(1683), 365–389.
Foale  S and Bishop  SR (1992), Dynamical complexities of forced impacting systems, Philos. Trans. R. Soc. London, Ser. A A338(1651), 547–556.
Bishop  SR (1994), Impact oscillators, Philos. Trans. R. Soc. London, Ser. A A347(1683), 347–351.
Hinrichs  N, Oestreich  M, and Popp  K (1997), Dynamics of oscillators with impact and friction, Chaos, Solitons, Fractals 8(4), 535–558.
Hinrichs  N, Oestreich  M, and Popp  K (1998), On the modeling of friction oscillators, J. Sound Vib. 216(3), 435–459.
Popp  K (1998), Non-smooth mechanical systems-an overview, Forschung im Ingenieurwesen 64, 223–239.
Haessig  DA and Friedland  B (1991), On the modeling and simulation of friction, ASME J. Dyn. Syst., Meas., Control 113, 354–362.
Armstrong-Hélouvry B (1991), Control of Machines with Friction, Kluwer Academic Publ, Boston.
Armstrong-Hélouvry  B (1993), Stick slip and control in low-speed motion, IEEE Trans. Autom. Control 38(10), 1483–1496.
Armstrong-Hélouvry  B, Dupont  P, and Canudas de Wit  C (1994), Friction in servo machines: Analysis and control methods, Appl. Mech. Rev. 47(7), 275–305.
Armstrong-Hélouvry  B, Dupont  P, and Canudas de Wit  C (1994), A survey of models, analysis tools and compensation methods for control of machines with friction, Automatica 30(7), 1083–1138.
Canudas de Wit  C, Olsson  H, Åström  KJ, and Lischinsky  P (1995), A new model for control of systems with friction, IEEE Trans. Autom. Control 40(3), 419–425.
Canudas de Wit C and Tsiotras P (1999), Dynamic tire friction model for vehicle traction control, Proc of 38th Conf on Decision and Control, 3746–3751.
Taylor JH (1994), A modeling language for hybrid systems, Proc of the Joint Symp of Computer-Aided Control System Design, 337–344.
Taylor JH (1995), Rigorous handling of state events in matlab, Proc of IEEE Conf on Control Applications, 156–161.
Taylor JH and Kebede D (1995), Modeling and simulation of hybrid system, Proc of IEEE Conf on Decision and Control, 2685–2687.
Taylor JH (1999), Tools for Modeling and Simulation of Hybrid Systems-A Tutorial Guide, Univ of New Brunswick, available at http://www.unb.edu.ca/jtaylor/HS_software.html.
Hou  L and Michel  AN (1998), Stability theory for hybrid dynamical systems, IEEE Trans. Autom. Control 43(4), 461–474.
Mindlin  RD (1949), Compliance of elastic bodies in contact, ASME J. Appl. Mech. 16, 259–268.
Oden  JT and Pires  EB (1983), Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity, ASME J. Appl. Mech. 50, 67–76.
Oden  JT and Pires  EB (1983), Numerical analysis of certain contact problems with non-classical friction laws, Comput. Struct. 16, 471–478.
Oden  JT and Pires  EB (1984), Algorithms and numerical results for finite element approximations of contact problems with non-classical friction laws, Comput. Struct. 19(1-2), 137–147.
Greenwood  JA (1997), Adhesion of elastic solids, Proc. R. Soc. London, Ser. A A453, 1277–1297.
Adams  GG (1995), Self-excited oscillations of two elastic half-spaces sliding with a constant coefficient of friction, ASME J. Appl. Mech. 62, 867–872.
Adams  GG (1999), Dynamic motion of two elastic half-spaces in relative sliding without slipping, ASME J. Tribol. 121(3), 455–461.
Adams  GG (1998), Steady sliding of two elastic half-spaces with friction reduction due to interface stick-slip, ASME J. Appl. Mech. 65, 470–475.
Ruiz  C, Boddington  PHB, and Chen  KC (1984), An investigation of fatigue and fretting in a dovetail joint, Exp. Mech. 24, 208–217.
Ruiz C and Chen KC (1986), Life assessment of dovetail joints between blades and disks in aero-engines, Proc of Int Conf on Fatigue: Fatigue of Engineering Materials and Structures, Inst of Mech Eng, 187–194.
Nix  KJ and Lindley  TC (1988), The influence of relative slip range and contact material on the fretting fatigue properties of 3.5nicrmov rotor steel, Wear 125, 147–162.
Kuno  M, Waterhouse  RB, Nowell  D, and Hills  DA (1989), Initiation and growth of fretting fatigue cracks in the partial slip regime, Fatigue Fract. Eng. Mater. Struct. 12(5), 387–398.
Nowell  D and Hills  DA (1990), Crack initiation criteria in fretting contact, Wear 136, 329–343.
Waterhouse  RB (1992), Fretting fatigue, Int. Mater. Rev. 37(2), 77–97.
Hills  DA, Nowell  D, and O’Connor  JJ (1988), On the mechanics of fretting fatigue, Wear 125, 129–146.
Bramhall R (1973), Studies in Fretting Fatigue, PhD thesis, Oxford Univ.
Hills  DA (1994), Mechanics of fretting fatigue, Wear 175, 107–113.
Cattaneo  C (1938), Sul contatto di due corpi elastici: Distribuzione locale degli sforzi, Rendiconti dell’Accademia Nazionale dei Lincei 27, 342–348, 434–436, 474–478.
Nowell  D and Hills  DA (1987), Mechanics of fretting fatigue tests, Int. J. Mech. Sci. 29(5), 355–365.
Szolwinski  MP and Farris  TN (1996), Mechanics of fretting fatigue crack formation, Wear 198, 93–107.
Söderberg  S, Bryggman  U, and McCullough  T (1986), Frequency effects in fretting wear, Wear 110, 19–34.
Bryggman  U and Söderberg  S (1986), Contact conditions in fretting, Wear 110, 1–17.
Bryggman  U and Söderberg  S (1988), Contact conditions and surface degradation mechanisms in low amplitude fretting, Wear 125, 39–52.
Vingsbo  O and Söderberg  S (1988), On fretting maps, Wear 126, 131–147.
Schouterden  K, Blanpain  B, Çelis  JP, and Vingsbo  O (1995), Fretting of titanium nitride and diamond-like carbon coatings at high frequencies and low amplitude, Wear 181–183, 86–93.
Rehbein  P and Wallaschek  J (1998), Friction and wear behavior of polymer/steel and alumina/alumina under high-frequency fretting conditions, Wear 216, 97–105.
Caughey  TK (1960), Sinusoidal excitation of a system with bilinear hysteresis, ASME J. Appl. Mech. 27, 640–643.
Caughey  TK (1960), Random excitation of a system with bilinear hysteresis, ASME J. Appl. Mech. 27, 649–652.
Iwan  WD (1965), The steady-state response of a two-degree-of-freedom bilinear hysteretic system, ASME J. Appl. Mech. 32, 151–156.
Iwan  WD (1965), The steady-state response of a double bilinear hysteretic model, ASME J. Appl. Mech. 32, 921–925.
Iwan WD (1965), The dynamic response of the one-degree-of-freedom bilinear hysteretic system, Proc of 3rd World Congress on Earthquake Engineering, 2 , 783–796.
Iwan  WD (1966), A distributed-element model for hysteresis and its steady-state dynamic response, ASME J. Appl. Mech. 33, 893–900.
Iwan  WD (1967), On a class of models for the yielding behavior of continuous and composite systems, ASME J. Appl. Mech. 34, 612–617.
Masing  G (1923–1924), Zur hevnschen theorie der verfestigung der metalle durch verborgene elastische spannungen, (in German), Wiss. Veröffent. aus dem Siemens Konzern 3, 135–141.
Byerlee  JD and Brace  WF (1968), Stick-slip, stable sliding, and earthquakes-effect of rock type, pressure, strain rate and stiffness, J. Geophys. Res. 73, 6031–6037.
Byerlee  JD (1970), The mechanics of stick-slip, Tectonophysics 9, 475–486.
Dieterich  JH (1978), Time-dependent friction and the mechanisms of stick-slip, Pure Appl. Geophys. 116, 790–806.
Dieterich  JH (1979), Modeling of rock friction 1: Experimental results and constitutive equations, J. Geophys. Res. 84, 2161–2168.
Dieterich  JH (1979), Modeling of rock friction 2: Simulation of preseismic slip, J. Geophys. Res. 84, 2169–2175.
Ruina  AL (1983), Slip instability and state variable friction laws, J. Geophys. Res. 88, 10359–10370.
Ruina  AL (1986), Unsteady motions between sliding surfaces, Wear 113, 83–86.
Linker  M and Dieterich  JH (1992), Effects of variable normal stress on rock friction: Observations and constitutive equations, J. Geophys. Res., [Solid Earth] 97, 4923–4940.
Rice  JR (1993), Spatio-temporal complexity of slip on a fault, J. Geophys. Res., [Solid Earth] 98(B6), 9885–9907.
Ben-Zion  Y and Rice  JR (1997), Dynamic simulations of slip on a smooth fault in an elastic solid, J. Geophys. Res., [Solid Earth] 102(B8), 17771–17784.
Persson BNJ (2000), Sliding Friction: Physical Principles and Applications, Second Edition, Springer-Verlag.
Mindlin  RD and Dereciewicz  H (1953), Elastic spheres in contact under varying oblique forces, ASME J. Appl. Mech. 20, 327–344.
Goodman  LE and Brown  CB (1962), Energy dissipation in contact friction: Constant normal and cyclic tangential loading, ASME J. Appl. Mech. 29, 17–22.
Johnson  KL (1961), Energy dissipation at spherical surfaces in contact transmitting oscillating forces, J. Mech. Eng. Sci. 3(4), 362–368.
Shaw  SW (1986), On the dynamic response of a system with dry friction, J. Sound Vib. 108(2), 305–325.
Beards  CF and Woohat  A (1985), The control of frame vibrations by friction damping in joints, ASME J. Vib., Acoust., Stress, Reliab. Des. 106, 26–32.
Ferri AA and Heck BS (1995), Vibration analysis of dry friction damped turbine blades using singular perturbation theory, Proc of ASME Int Mech Eng Congress and Exposition, AMD-Vol 192, ASME, New York, 47–56.
Griffin  JH (1980), Friction damping of resonant stresses in gas turbine engine airfoils, ASME J. Eng. Power 102, 329–333.
Pierre  C, Ferri  AA, and Dowell  EH (1985), Multi-harmonic analysis of dry friction damped systems using an incremental harmonic balance method, ASME J. Appl. Mech. 52, 958–964.
Wang  JH and Chen  WK (1993), Investigation of the vibration of a blade with friction damper by hbm, ASME J. Eng. Gas Turbines Power 115, 294–299.
Dowell  EH (1986), Damping in beams and plates due to slipping at the support boundaries, J. Sound Vib. 105(2), 243–253.
Dowell  EH and Schwartz  HB (1983), Forced response of a cantilever beam with dry friction damper attached, Part I: Theory, J. Sound Vib. 91(2), 255–267.
Dowell  EH and Schwartz  HB (1983), Forced response of a cantilever beam with dry friction damper attached, Part II: Experiment, J. Sound Vib. 91(2), 269–291.
Ferri  AA and Bindemann  AC (1992), Damping and vibration of beams with various types of frictional support conditions, ASME J. Vibr. Acoust. 114, 289–296.
Makris  N and Constantinou  MC (1991), Analysis of motion resisted by friction, I. constant coulomb and linear/coulomb friction, Mech. Struct. Mach. 19(4), 477–500.
Makris  N and Constantinou  MC (1991), Analysis of motion resisted by friction, II. Velocity-dependent friction, Mech. Struct. Mach. 19(4), 501–526.
Gaul  L and Nitsche  R (2001), The role of friction in mechanical joints, Appl. Mech. Rev. 54(2), 93–105.
Gaul  L and Nitsche  R (2000), Friction control for vibration suppression, Mech. Syst. Signal Process. 14(2), 139–150.
Gaul  L and Lenz  J (1997), Nonlinear dynamics of structures assembled by bolted joints, Acta Mech. 125(1–4), 169–181.
Lenz J and Gaul L (1995), The influence of microslip on the dynamic behavior of bolted joints, Proc of 13th Int Modal Analysis Conf, Nashville, TN, 248–254.
Johnson KL (1985), Contact Mechanics, Cambridge Univ Press, Great Britain.
Sinha  A and Griffin  JH (1984), Effects of static friction on the forced response of frictionally damped turbine blades, ASME J. Eng. Gas Turbines Power 106, 65–69.
Griffin  JH and Sinha  A (1985), The interaction between mistuning and friction in the forced response of bladed disk assemblies, ASME J. Eng. Gas Turbines Power 107, 205–211.
Menq  C-H and Griffin  JH (1985), A comparison of transient and steady state finite element analyses of the forced response of a frictionally damped beam, ASME J. Vib., Acoust., Stress, Reliab. Des. 107, 19–25.
Menq  C-H, Griffin  JH, and Bielak  J (1986), The influence of a variable normal load on the forced vibration of a frictionally damped structure, ASME J. Eng. Gas Turbines Power 108, 300–305.
Menq  C-H, Bielak  J, and Griffin  JH (1986), The influence of microslip on vibratory response, part i: A new microslip model, J. Sound Vib. 107(2), 279–293.
Cameron TM, Griffin JH, Kielb RE, and Hoosac TM (1987), An integrated approach for friction damper design, ASME Design Booklet, The Role of Damping in Vibration and Noise Control, ASME DE-Vol 5, 205–211.
Kielb RE, Griffin JH, and Menq C-H (1988), Evaluation of a turbine blade damper using an integral approach, AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf (AIAA 88-2400), 1495–1500.
Muszynska  A and Jones  DIG (1983), A parametric study of dynamic response of a discrete model of turbomachinery bladed disk, ASME J. Vib., Acoust., Stress, Reliab. Des. 105, 434–443.
Wang  JH and Shieh  WL (1991), The influence of variable friction coefficient on the dynamic behavior of a blade with friction damper, J. Sound Vib. 149, 137–145.
Sanliturk  KY, Imregun  M, and Ewins  DJ (1997), Harmonic balance vibration analysis of turbine blades with friction dampers, ASME J. Vibr. Acoust. 119, 96–103.
Sanliturk  KY and Ewins  DJ (1996), Modeling two-dimensional friction contact and its application using harmonic balance method, J. Sound Vib. 193, 511–523.
Whitehouse  DJ and Archard  JF (1970), The properties of random surfaces of significance in their contact, Proc. R. Soc. London, Ser. A A316(1524), 97–121.
Whitehouse  DJ and Phillips  MJ (1978), Discrete properties of random surfaces, Philos. Trans. R. Soc. London, Ser. A A290(1369), 267–298.
Whitehouse  DJ and Phillips  MJ (1982), Two-dimensional discrete properties of random surfaces, Philos. Trans. R. Soc. London, Ser. A A305(1490), 441–468.
Kilburn  RF (1974), Friction viewed as a random process, J. Lubr. Technol. 96, 291–299.
Qiao  SL and Ibrahim  RA (1999), Stochastic dynamics of systems with friction-induced vibration, J. Sound Vib. 223(1), 115–140.
Ibrahim  RA, Zielke  SA, and Popp  K (1999), Characterization of interfacial forces in metal-to-metal contact under harmonic excitation, J. Sound Vib. 220(2), 365–377.
Ibrahim  RA, Madhavan  S, Qiao  SL, and Chang  WK (2000), Experimental investigation of friction-induced noise in disc brake systems, Int. J. Veh. Des. 23(3/4), 218–240.
Mottershead  JE, Ouyang  H, Cartmell  MP, and Friswell  MI (1997), Parametric resonances in an annular disc, with a rotating system of distributed mass and elasticity; and the effects of friction and damping, Proc. R. Soc. London, Ser. A A453(1956), 1–19.
Ouyang  H, Mottershead  JE, Cartmell  MP, and Friswell  MI (1998), Friction-induced parametric resonances in discs: Effect of a negative friction-velocity relationship, J. Sound Vib. 209(2), 251–264.
Ouyang  H, Mottershead  JE, Cartmell  MP, and Brookfield  DJ (1999), Friction-induced vibration of an elastic slider on a vibrating disc, Int. J. Mech. Sci. 41, 325–336.
Ouyang  H, Mottershead  JE, Brookfield  DJ, and James  S (2000), A methodology for the determination of dynamic instabilities in a car disc brake, Int. J. Veh. Des. 23(3/4), 241–262.
Lee  D and Waas  AM (1997), Stability analysis of a rotating multi-layer annular plate with a stationary frictional follower load, Int. J. Mech. Sci. 39(10), 1117–1138.
Brooks PC, Crolla DA, and Lang AM (1992), Sensitivity analysis of disc brake squeal, Proc of Int Symp on Advanced Vehicle Control, (AVEC’92), Yokohama, Japan, Paper No. 923005, 28–36.
Brooks PC, Crolla DA, Lang AM, and Schafer DR (1993), Eigenvalue sensitivity analysis applied to disc brake squeal, Braking of Road Vehicles, Paper C444/004/93, Inst of Mech Eng, 135–143.
Lang AM, Schafer DR, Newcomb TP, and Brooks PC (1993), Brake squeal-the influence of rotor geometry, Braking of Road Vehicles, Paper C444/016/93, Inst of Mech Eng, 161–171.
Carpick  RW and Salmeron  M (1997), Scratching the surface: Fundamental investigations of tribology with atomic force microscopy, Chem. Rev. 97, 1163–1194.
Bhushan  B, Isrealachvili  JN, and Landman  U (1995), Nanotribology: Friction, wear and lubrication at the atomic scale, Nature (London) 374, 607–616.
Bhushan  B (1999), Nanoscale tribophysics and tribomechanics, Wear 225–229, 465–492.
Johnson  KL, Kendall  K, and Roberts  AD (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London, Ser. A A324, 301–313.
Tabor  D (1977), Surface forces and surface interactions, J. Colloid Interface Sci. 58, 2–13.
Johnson  KL and Greenwood  JA (1997), An adhesion map for the contact of elastic spheres, J. Colloid Interface Sci. 192, 326–333.
Israelachvili  JN (1992), Adhesion forces between surfaces in liquids and condensable vapours, Surf. Sci. Rep. 14(3), 109–159.
Yoshizawa  H, McGuiggan  P, and Israelachvili  JN (1993), Identification of a second dynamic state during stick-slip motion, Science 259, 1305–1308.
McClelland GM (1989), Adhesion and Friction, Springer Series in Surface Science, Springer, New York.
Yoshizawa  H, Chen  Y-L, and Israelachvili  JN (1993), Recent advances in molecular level understanding of adhesion, friction and lubrication, Wear 168, 161–166.
Yoshizawa  H and Israelachvili  JN (1993), Fundamental mechanisms of interfacial friction; stick-slip friction of spherical and chain molecules, J. Phys. Chem. 97, 11300–11313.
Mate  CM, McClelland  GM, Erlandsson  R, and Chiang  S (1987), Atomic-scale friction of a tungsten tip on a graphite surface, Phys. Rev. Lett. 59(17), 1942–1945.
Nayfeh AH (1981), Introduction to Perturbation Techniques, John Wiley and Sons, New York.
Karnopp  D (1985), Computer simulation of stick-slip friction in mechanical dynamic systems, ASME J. Dyn. Syst., Meas., Control 107(1), 100–103.
Pratt  TK and Williams  R (1981), Non-linear analysis of stick-slip motion, J. Sound Vib. 74, 531–542.
Hutchinson  JW and Jensen  HM (1990), Models of fiber debonding and pullout in brittle composites with friction, Mech. Mater. 9(2), 139–163.
Sextro W (1999), Forced vibration of elastic structures with friction contacts, Proc of ASME Design Eng Tech Conf, DETC/VIB-8180, ASME, New York.
Berger  EJ, Begley  MR, and Mahajani  M (2000), Structural dynamic effects on interface response—Formulation and simulation under partial slipping conditions, J. Appl. Mech. 67, 785–792.
Masri  SF, Chassiakos  AG, and Caughey  TK (1993), Identification of nonlinear dynamic systems using neural networks, J. Appl. Mech. 60(2), 123–133.


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Notation for parameter-dependent friction: a) velocity dependence, b) dwell time dependence, c) time lag, d) pre-slip displacement
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Contact system showing angular deflection for Vo≠0 (due to friction asymmetry)
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Schematic of Mindlin (partial slip) result for nominal Hertzian contact: contact half-width a and stick zone half-width c<a
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Variation of fatigue life in fretting contacts as a function of a) interface slip displacement ux and b) applied normal load Fn (after Vingsbo and Söderberg 110, Figs. 10 and 11 respectively)
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Lumped-parameter models for friction contact: a) macroslip (bilinear hysteresis) element, b) Iwan parallel-series model, c) Iwan series-parallel model
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Single-dof stick-slip oscillations, two possible cases: a) single-dof forced system, b) short stick response, c) long stick response
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SFA experiment schematic showing glass substrate, epoxy, and atomically-smooth mica sheets
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AFM experiment schematic: a) AFM cantilever and tip, with incident light for displacement measurement, b) AFM cantilever deformed shape
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Atomic-scale stick-slip response
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Single-dof structural model for study of self-excited problems
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Velocity-dependent friction curve showing dependence upon three independent parameters (μo1,α)
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Stability map for velocity-dependent friction and single-dof structural model
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Stability map for velocity-dependent friction and single-dof structural model, with time-dependent normal force: a) ε=0.001,b) ε=0.01
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Step-plus-evolutionary response of state-variable friction laws to step changes in sliding velocity
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Stability map in the (S⁁,V⁁,f⁁) parameter space: a family of stability boundaries (solid lines) above which the steady-sliding response is unstable; response is unconditionally unstable above dashed line
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Lumped-parameter (viscoelastic) model for rate- and state-dependent friction
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Stick-slip response: a) time history, b) phase plane
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Time response of friction coefficient in stick-slip oscillations
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Sample calculations from Shaw 135 showing frequency response of stick-slip oscillations with continuous amplitude curve through the stick-slip boundary
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Smoothing of friction discontinuity using an arctan-type approximation: mutli-valued friction at zero relative velocity (and therefore inclusion of true sticking) is neglected
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Three continuous systems with different boundary friction conditions: a) coulomb friction support, b) in-plane displacement-dependent normal force, c) out-of-plane displacement-dependent normal force (schematic from Ferri and Bindemann 144)
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Schematic of result from Ferri and Bindemann 144 showing hardening behavior with increasing contact angle (case II from Fig. 21b)
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Calibration of lumped-parameter partial slip models using monotonic loading and a collocation procedure at discrete points xcr,i (monotonic loading)
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Cyclic loading behavior of lumped-parameter partial slip models showing hysteresis (single-element model of Fig. 5a, multi-element model of Fig. 5b); pre-slip displacement for single-element model is shown
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Single-dof structural model with bilinear hysteresis friction damper
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Steady-state response x⁁(τ) under single-frequency excitation; damper sticks more than one-half of the time per forcing cycle yet x⁁(τ) is substantially harmonic
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Steady-state response amplitude X⁁ss and time-averaged percent sticking per forcing cycle variations with coupling parameter γ
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Damper mass effects on steady-state forced response. An example result from Ferri and Heck 137 showing a qualitative difference in predictions for massless (bilinear hysteresis) and non-zero-mass models.
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The Menq-Griffin two elastic bar partial slip model
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Menq-Griffin partial slip model characteristics (F1<F2<F3<F4)
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Comparison of Menq-Griffin partial slip model and bilinear hystersis model under monotonic loading
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Break-away behavior of elastic block on rigid support under monotonically-increasing tangential load; inset: schematic of system geometry and loading
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Comparison of friction modeling approaches against key performance criteria: ability to capture relevant problem physics, computational efficiency, and model fidelity



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