A Graphical Approach to Shakedown in Rolling Contact

  • K. L. Johnson

Abstract

In repeated rolling contact, even though plastic deformation may occur during the first passage of the load, through the action of residual stresses and strain hardening of material, the steady cyclic state may lie within the elastic limit. Using the Tresca yield criterion it is shown in this paper how the maximum stress for shakedown - the shakedown limit - in line contact may be found by a simple graphical procedure.

Cases of tractive rolling, with both partial and complete slip, are examined for (a) a perfectly-plastic and (b) a kinematically hardening material.

Keywords

Residual Stress Elastic Limit Yield Locus Rolling Contact Intermediate Principal Stress 
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References

  1. 1.
    Fessler, H., and Ollerton, E., Contact stresses in toroids under radial loads, Brit..1.Appl.Phvs. 1957, E, 387–393.Google Scholar
  2. 2.
    Lundberg, G., and Palmgren, A., Dynamic capacity of rolling bearings, Acta Polvtechnica. Stockholm, Mech.Eng.Series 1947, 1, 1–50.Google Scholar
  3. 3.
    Crook, A.W., Simulated gear-tooth contacts: some experiments on their lubriction and subsurface deformation, 1957, Proc,Ins t.Mech.Engrs. 171. 187–214.Google Scholar
  4. 4.
    Ziegler, H., A modification of Prager’s hardening rule, Quart. of Appl.Math 1959, 17, 55–65.Google Scholar
  5. 5.
    Melan, E., Der spannungsgudstand eines Henky-Mises schen Kontinuums bei Verlandicher Belastung, Sitzungberichte der Ak. Wissenschaften Wien, Ser. 2A, 1938, 147, 73.Google Scholar
  6. 6.
    Ponter, A.R.S., A general shakedown theorem for elastic-plastic bodies with work hardinng, 3rd Int.Conf. on Structural Mechainics in Reactor Tech., London, 1976.Google Scholar
  7. 7.
    Johnson, K.L., Contact Mechnics. C.U.P., Cambridge 1985, pp. 103–205 and 429.Google Scholar
  8. 8.
    Johnson, K.L., A shakedown limit in rolling contact, Proc. 4th US Nat.Conference of Appl.Mech., Berkeley, 1962, ASME.Google Scholar
  9. 9.
    Johnson, K.L., and Jefferis, J.A., Plastic flow and residual stresses in rolling and sliding contact. Proc.Inst.of Mech.Engrs. Symposium on Rolling Contact Fatigue. London, p. 50.Google Scholar
  10. 10.
    Bower, A.F., and Johnson, K.L., The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contacts’, 1989 J.M.P.S., 37, 471–493.Google Scholar
  11. 11.
    Carter, F.W., On the action of a locomotive driving wheel, Proceedings. Royal Society. A112, 151.Google Scholar
  12. 12.
    Haines D.J. and Ollerton, E., Contact stress distributions on elliptical contact surfaces subjected to radial and tangential forces, Proceedings. Institution of Mechanical Engineers. 177. 95.Google Scholar

Copyright information

© Elsevier Science Publishers Ltd 1990

Authors and Affiliations

  • K. L. Johnson
    • 1
  1. 1.Cambridge University Engineering LaboratoryCambridgeUK

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