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Full Assessment of Micromachine Friction Within the Rate-State Framework: Theory and Validation

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Abstract

Model parameters are extracted from the experimental results in a companion paper (Shroff and de Boer in Tribol Lett 63(3):31, 2016) according to rate-state friction theory. Perturbation theory and state-space modeling are used to compare predictions for the stick–slip to steady sliding bifurcation line with experimental results using these extracted parameters. The line is well predicted in k/N b − v p space. The average behavior of the stick–slip oscillations is in good agreement with the state-space simulations. We estimate the memory length d c using a state-space model and find that it lies between the monoplane chain length and the average asperity diameter. This work indicates that rate-state theory extends from the µm scale to the nm scale in the few contacts situation.

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References

  1. Heslot, F., Baumberger, T., Perrin, B., Caroli, B., Caroli, C.: Creep, stick-slip, and dry-friction dynamics: experiments and a heuristic model. Phys. Rev. E 49(6), 4973 (1994)

    Article  Google Scholar 

  2. Shroff, S.S., de Boer, M.P.: Full assessment of micromachine friction within the rate-state framework: experiments. Tribol. Lett. 63(3), 31 (2016). doi:10.1007/s11249-016-0718-3

    Article  Google Scholar 

  3. Dieterich, J.H., Kilgore, B.D.: Direct observation of frictional contacts: new insights for state-dependent properties. Pure Appl. Geophys. 143(1–3), 283–302 (1994)

    Article  Google Scholar 

  4. Carlson, J.M., Batista, A.A.: Constitutive relation for the friction between lubricated surfaces. Phys. Rev. E 53(4), 4153 (1996)

    Article  Google Scholar 

  5. Lim, Y.F., Chen, K.: Dynamics of dry friction: a numerical investigation. Phys. Rev. E 58(5), 5637 (1998)

    Article  Google Scholar 

  6. Shroff, S.S., Ansari, N., Ashurst, W.R., de Boer, M.P.: Rate-state friction in microelectromechanical systems interfaces: experiment and theory. J. Appl. Phys. 116(24), 244902 (2014)

    Article  Google Scholar 

  7. Srinivasan, U., Houston, M.R., Howe, R.T., Maboudian, R.: Alkyltrichlorosilane-based self-assembled monolayer films for stiction reduction in silicon micromachines. J. Microelectromech. Syst. 7(2), 252–260 (1998)

    Article  Google Scholar 

  8. Yoshizawa, H., Chen, Y.L., Israelachvili, J.: Fundamental mechanisms of interfacial friction. 1. Relation between adhesion and friction. J. Phys. Chem. 97(16), 4128–4140 (1993)

    Article  Google Scholar 

  9. Yoshizawa, H., Israelachvili, J.: Fundamental mechanisms of interfacial friction. 2. Stick-slip friction of spherical and chain molecules. J. Phys. Chem. 97(43), 11300–11313 (1993)

    Article  Google Scholar 

  10. Ruina, A.: Slip instability and state variable friction laws. J. Geophys. Res. 88(B12), 10359–10370 (1983)

    Article  Google Scholar 

  11. Ruina, A.: Stability of steady frictional slipping. J. Appl. Mech. 50, 343–349 (1983)

    Article  Google Scholar 

  12. Drummond, C., Israelachvili, J.: Dynamic behavior of confined branched hydrocarbon lubricant fluids under shear. Macromolecules 33(13), 4910–4920 (2000)

    Article  Google Scholar 

  13. De Wit, C.C., Olsson, H., Astrom, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995)

    Article  Google Scholar 

  14. Dieterich, J.H.: Modeling of rock friction: 1. Experimental results and constitutive equations. J. Geophys. Res. 84(B5), 2161–2168 (1979)

    Article  Google Scholar 

  15. Scholz, C.H.: The Mechanics of Earthquakes and Faulting. Cambridge University Press (2002)

  16. Sniegowski, J.J., de Boer, M.P.: IC-compatible polysilicon surface micromachining. Annu. Rev. Mater. Sci. 30(1), 299–333 (2000)

    Article  Google Scholar 

  17. Corwin, A.D., de Boer, M.P.: Effect of adhesion on dynamic and static friction in surface micromachining. Appl. Phys. Lett. 84(13), 2451–2453 (2004)

    Article  Google Scholar 

  18. Ben-David, O., Rubinstein, S.M., Fineberg, J.: Slip-stick and the evolution of frictional strength. Nature 463(7277), 76–79 (2010)

    Article  Google Scholar 

  19. Kosterin, L., Kragelskii, I.: Relaxation oscillations in elastic friction systems. ASME 12, 111–134 (1960). (Friction and Wear in Machinery)

    Google Scholar 

  20. Gu, J.-C., Rice, J.R., Ruina, A.L., Tse, S.T.: 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 (1984)

    Article  Google Scholar 

  21. Bar-Sinai, Y., Spatschek, R., Brener, E.A., Bouchbinder, E.: On the velocity-strengthening behavior of dry friction. J. Geophys. Res. Solid Earth 119(3), 1738–1748 (2014)

    Article  Google Scholar 

  22. Kiely, J., Houston, J.: Contact hysteresis and friction of alkanethiol self-assembled monolayers on gold. Langmuir 15(13), 4513–4519 (1999)

    Article  Google Scholar 

  23. Persson, B.N.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61(4), 201–227 (2006)

    Article  Google Scholar 

  24. Rubinstein, S.M., Cohen, G., Fineberg, J.: Detachment fronts and the onset of dynamic friction. Nature 430(7003), 1005–1009 (2004)

    Article  Google Scholar 

  25. Gee, M.L., McGuiggan, P.M., Israelachvili, J.N., Homola, A.M.: Liquid to solidlike transitions of molecularly thin films under shear. J. Chem. Phys. 93(3), 1895–1906 (1990)

    Article  Google Scholar 

  26. Bhushan, B., Israelachvili, J.N., Landman, U.: Nanotribology: friction, wear and lubrication at the atomic scale. Nature 374(6523), 607–616 (1995)

    Article  Google Scholar 

  27. Grillo, S., Ducarroir, M., Nadal, M., Tournie, E., Faurie, J.: Nanoindentation of Si, GaP, GaAs and ZnSe single crystals. J. Phys. D Appl. Phys. 36(1), L5 (2003)

    Article  Google Scholar 

  28. Tuck, K., Jungen, A., Geisberger, A., Ellis, M., Skidmore, G.: A study of creep in polysilicon MEMS devices. J. Eng. Mater. Technol. 127(1), 90–96 (2005)

    Article  Google Scholar 

  29. Tas, N., Wissink, J., Sander, L., Lammerink, T., Elwenspoek, M.: Modeling, design and testing of the electrostatic shuffle motor. Sens. Actuators A 70(1), 171–178 (1998)

    Article  Google Scholar 

  30. Tas, N., Gui, C., Elwenspoek, M.: Static friction in elastic adhesion contacts in MEMS. J. Adhes. Sci. Technol. 17(4), 547–561 (2003)

    Article  Google Scholar 

  31. Corwin, A.D., de Boer, M.P.: Frictional aging and sliding bifurcation in monolayer-coated micromachines. J. Microelectromech. Syst. 18(2), 250–262 (2009)

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Science Foundation (NSF) under Grant CMMI 1030322. The work of S.S.S. was supported by the NSF Graduate Research Fellowship Program. The authors thank the staff of Sandia National Laboratories Microelectronics Development Laboratory for the fabrication of the devices used in these experiments and one of the reviewers for pointing out the applicability of Eq. (10).

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  1. Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Sameer S. Shroff & Maarten P. de Boer

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  1. Sameer S. Shroff
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  2. Maarten P. de Boer
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Correspondence to Maarten P. de Boer.

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Shroff, S.S., de Boer, M.P. Full Assessment of Micromachine Friction Within the Rate-State Framework: Theory and Validation. Tribol Lett 63, 39 (2016). https://doi.org/10.1007/s11249-016-0724-5

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