Method of Dimensionality Reduction in Contact Mechanics and Friction by Valentin L. Popov & Markus Heß

Author:Valentin L. Popov & Markus Heß
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(8.38)

for which denotes the normal stress distribution and the normal force distribution. The heat flows into both half-spaces respectively according to

(8.39)

The distribution between the two sometimes causes difficulties, because the weighted function is generally dependent on x and y in order not to violate the continuity of the temperature within the contact area [9]. We circumvent the problem by assuming that one of the contacts is non-conductive, so that the entire heat flows into the other body. We would now like to determine the temperature distribution on the surface of this body by using the reduction method; its specific thermal conductivity is . We consider an element of the linearly elastic foundation with the coordinate that is indented by . The known force acting on this element is then . The frictional power of the element is for which the resulting temperature difference of the element is

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