Since worn wheels and rails contact conformally, the existing contact stress theories for nonconformal contact are not adequate. In this report a general numerical method of solution for three dimensional, frictionless, conformal, elastic contact problems is presented for the first time. The method is used to analyze the conformal contact of a sphere indenting a spherical seat and a cylinder indenting a cylindrical seat. The results of the sphere-spherical seat problem compared well with experimental data. Results of the cylinder-cylindrical seat problem were in close agreement to a known analytic solution of this problem. For both analyses, results compared favorably with Hertzian theory for problems with small contact regions. A method is given for defining the boundaries of the large contact regions, and for solving the associated governing singular integral equation of the first kind. A general iterative procedure is developed which converges to the true three dimensional contact region. In addition the solution to a non-Hertzian contact problem with a multiply connected contact region is solved; namely, the case of two spheres in contact where one of them has a surface defect or pit.

  • Supplemental Notes:
    • Sponsored by the U.S. DOT's Office of the Secretary, Program for University Research. Technical Monitor for the study was Clifford Gannett, Office of the Secretary, U.S. DOT. See also report dated 22 Apr 75, PB-251238.
  • Corporate Authors:

    University of Pennsylvania, Philadelphia

    Department of Mechanical Engineering and Applied Mechanics
    Philadelphia, PA  United States  19104

    Department of Transportation

    Office of University Research, 1200 New Jersey Avenue, SE
    Washington, DC  United States  20590
  • Authors:
    • Woodward, W
    • Paul, B
  • Publication Date: 1976-12

Media Info

  • Features: References;
  • Pagination: 272 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00163784
  • Record Type: Publication
  • Source Agency: Department of Transportation
  • Report/Paper Numbers: DOT-TST-77-48 Final Rpt.
  • Contract Numbers: DOT-OS-40093
  • Files: TRIS, USDOT
  • Created Date: Oct 29 1977 12:00AM