A mathematical model is developed for the condition where turbine blade/shroud contact occurs at discrete patches on the shroud. The contact patch is treated as having uniform time-mean contact pressure; and several components of relative displacement are identified, these having to sum to zero in the contact patch to assure an unbroken interface in the patch. Operating conditions which meet this requirement permit the postulated patchlike contact to exist. Operating conditions which do not meet it will not be associated with such patches. The components of relative displacement are almost independent of one another and are treated as linearly additive. These are: (1) thermal expansion of the shroud material in the patch, (2) elastic indentation of the shroud by the blade tip, (3) wear of the shroud material, (4) wear of the blade tip, (5) dynamic displacement of the blade tip, (6) dynamic displacement of the shroud, (7) elastic compression of the thinned blade tip portion. Using these components and applying the foregoing condition for full contact, the speed at which the contact patch traverses along the shroud surface is solved for, and the factors which determine the width of the contact patch are determined.

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