Machinery

Download Elements of Friction Theory and Nanotribology by Enrico Gnecco PDF

By Enrico Gnecco

ISBN-10: 1107006236

ISBN-13: 9781107006232

Combining the classical theories of touch mechanics and lubrication with the learn of friction at the nanometer diversity, this multi-scale booklet for researchers and scholars alike courses the reader deftly during the mechanisms governing friction techniques, in keeping with state of the art types and experimental effects. the 1st ebook within the box to include contemporary study on nanotribology with classical theories of touch mechanics, this distinctive textual content explores atomic scale scratches, non-contact friction and fishing of molecular nanowires as saw within the lab. starting with uncomplicated key thoughts, the reader is guided via an increasing number of complicated issues, corresponding to touch of self-affine surfaces and nanomanipulation, in a constant variety, encompassing either macroscopic and atomistic descriptions of friction, and utilizing unified notations to allow use by means of physicists and engineers around the medical group.

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Extra info for Elements of Friction Theory and Nanotribology

Sample text

Ux = ∓ (1 − 2ν) pa. 7) Again, these conclusions change if the 2D system is finite. Circular loading If a uniform pressure p is applied to a circular region of radius a on an elastic half-space, the normal displacement is distributed as in Fig. 4. 4]. Outside the circle: uz = − 2(1 − ν) pr a a2 E − 1− 2 πG r r K a r (r > a). The radial displacement inside the circle is proportional to r : ur = − (1 − 2ν) pr 4G (r < a). 1 The functions K and E are defined as K (k) = π/2 0 dθ 1 − k 2 sin2 θ , E(k) = π/2 0 1 − k 2 sin2 θ dθ.

3) πG Note that the logarithmic divergence is typical of infinite problems in 2D and is removed if the sample has a finite size. The lateral displacement is constant and given by (1 − 2ν) f N ux = ∓ . 5] (Fig. 3). The maximum shear stress τmax peaks on the semi-circle with diameter 2a, where it reaches the value p/π . 1) on the loaded area and differentiating with respect to z. As a result: uz = (1 − ν) x p (a + x) ln 1 + 2π G a 2 + (a − x) ln 1 − x a 2 + const. 6) Inside the strip the tangential displacement u x is proportional to the distance x from the axis.

7) Again, these conclusions change if the 2D system is finite. Circular loading If a uniform pressure p is applied to a circular region of radius a on an elastic half-space, the normal displacement is distributed as in Fig. 4. 4]. Outside the circle: uz = − 2(1 − ν) pr a a2 E − 1− 2 πG r r K a r (r > a). The radial displacement inside the circle is proportional to r : ur = − (1 − 2ν) pr 4G (r < a). 1 The functions K and E are defined as K (k) = π/2 0 dθ 1 − k 2 sin2 θ , E(k) = π/2 0 1 − k 2 sin2 θ dθ.

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