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    Analytical Determination of Normal Contact Stresses for Arbitrary Geometries with Application to the Tire/Pavement Interaction Mechanism

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    A method for approximating the normal contact pressure distribution and the contact length associated with tire/pavement interaction has been developed using deformed tire geometry as a measured function of position. The mathematical development of the method is based on classic contact stress theory for contact between an elastic half plane and a rigid indenter. The unknown pressure distribution satisfies a linear integral equation and is approximated by an M-order polynomial with M + 1 unknown coefficients. The unknown coefficients are found by evaluation of both sides of the integral equation at M + 1 points, and the polynomial pressure distribution is plotted. The order, M, of the pressure distribution polynomial is sequentially increased until the pressure distribution stabilizes, completing the solution process. The contact length is approximated from sign changes in the pressure distribution caused by the geometric characteristics of the deformation curve for the tire not in contact with the pavement surface.

    Polynomial approximations for the pressure distributions compare favorably with the analytical pressure distributions for arc-shaped and triangular indenters. The approximated contact lengths are within 10% of those measured experimentally. These results provide basic verification of the approximation method. The information available through this method is essential for the generation of realistic time-fluctuating force inputs into analytical vibration response models when predicting tire vibration response on various types of pavement surfaces.


    tire/pavement interaction, contact stress, contact length, tire vibration, roughness

    Author Information:

    Clapp, TG
    Research assistant, North Carolina State University, Raleigh, NC

    Kelley, CT
    Associate professor, North Carolina State University, Raleigh, NC

    Eberhardt, AC
    Associate professor, North Carolina State University, Raleigh, NC

    Committee/Subcommittee: E17.21

    DOI: 10.1520/STP34600S