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A New Solution for the Two-Zonal Contact Problem

  • Research Article - Mechanical Engineering
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Abstract

Multi-zonal contact problems are defined as a unique contact problem with more than one contact zone. In this category of problem, the individual contact zones are close enough to affect each other. In this study, a symmetric two-zonal contact problem is solved analytically as a problem of rigid profile contact with an elastic half plane. Contact pressure function is obtained using the general form of contact pressure function introduced by Muskhelishvili (Some basic problems of the mathematical theory of elasticity, Noordoff Ltd, The Netherland, 1963) but new method is used to simplify the calculation procedure that makes it possible to find complete form of the answer (real and imaginary parts together). Complete form of the contact pressure function is necessary to use a recently introduced relation by Adib Nazari et al. (Int. J. Mater. Des. 29:818–828, 2008) to find Muskhelishvili potential function. This relation is used to calculate the new form of the Muskhelishvili potential function for a two-zonal contact problem and it is the first time used for a multi-zonal contact problem. All of the results are compared with FEM; while two-zonal contact pressure function is validated by Hertz contact pressure function. A complete analysis is accomplished in the nature of two-zonal contact problem and vicinity effect of two separate contact zones is achieved in maximum pressure status. Derived relations can be used to simulate any two-zonal contact with convex contact profiles. Multi-zonal contact situations have numerous applications in mechanical designing such as cutting tools. Also determining stress filed in these situations is useful in aging procedures.

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Abbreviations

L K = [a k b k ],:

Contact zones in a multi-zonal

k = 1. . . n :

contact problem

P :

Pressure load applied to elastic half plane through the contact by rigid profile

Q :

Shear load applied to elastic half plane through the contact by rigid profile

p(x):

Normal stress in the surface of elastic half plane

τ xy (x, 0):

Tangential stress in the surface of elastic half plane

n :

Number of contact zones

P n-1 (t 0):

Arbitrary polynomial of degree n−1

f(t):

Contact profile or rigid profile function

f′(t):

Derivative of the rigid profile function

μ :

Shear modulus

ν :

Poisson’s ratio

Φ(z):

Muskhelishvili potential function or stress function

a, b :

Contact zone ends

2C :

Distance between two punches or rigid profiles

R :

Contact zone curvature

P 0 :

Value of external applied load

t pmax :

Point of maximum pressure

2l :

Length of the single contact zone

References

  1. Hills, D.A.; Sackfield, A.: Mechanics of Elastic Contacts, Butterworth-Heinemann, Oxford (1993)

  2. Adib Nazari S., Naderi D., Sharafbafi F: Analytical solution for contact problem between a tilted wedge and half-plane under partial slip condition. Int. J. Mater. Des. 29, 1291–1299 (2008)

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  3. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordoff Ltd, Netherland (1963)

  4. Gladwell, G.M.L.: Contact Problems in the Classical Theory of Elasticity, p. 556. Sijthoff and Noordhoff, Rockville (1980)

  5. Ciavarella, M.; Demelio, G.; Murolo, C.: A numerical algorithm for the solution of two-dimensional rough contact problems. J. Strain Anal. Eng. Des. 0309-3247 (2005)

  6. Wang, Z.J.; Meng, F.M.; Xiao, K.; Wang, J.X.; Wang, W.Z.: Numerical analysis of partial slip contact under a tangential force and a twisting moment. J. Eng. Tribol. doi:10.1177/2041305X10392125 (2010)

  7. Adib Nazari S., Sharafbafi F., Naderi D: Determination of potential function for uncoupled-plane contact problems. Int. J. Mater. Des. 29, 818–828 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Khorasan Science and Technology Park, Mashhad, Iran

    M. Dezyani

  2. Iran Air Company, Tehran, Iran

    F. Sharafbafi

  3. Faculty of Aerospace Engineering, K.N.T. University of Technology, Tehran, Iran

    S. Irani

Authors
  1. M. Dezyani
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  2. F. Sharafbafi
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  3. S. Irani
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Corresponding author

Correspondence to M. Dezyani.

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Dezyani, M., Sharafbafi, F. & Irani, S. A New Solution for the Two-Zonal Contact Problem. Arab J Sci Eng 38, 1509–1518 (2013). https://doi.org/10.1007/s13369-013-0540-2

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  • DOI: https://doi.org/10.1007/s13369-013-0540-2

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