同じ表面形をもつ凸面と凹面との間のしぼり膜について

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The problem of fluid film squeezing between convex and concave walls of the same curvature is studied theoretically. Their shapes are arbitrary but axisymmetric, and they are installed coaxially. One wall is fixed and the other is moving along its axis with an arbitrary velocity. Assuming that the ratio of the gap between the two walls to their radii is small, an approximate solution of Navier-Stokes equation is found in the form of the power series of the ratio with precision up to the third order. In order to confirm the accuracy of the approximate solution, it is compared with a numerical solution for the case of flat walls. They agree with each other. It is found that the results obtained numerically by other workers can be derived easily from the approximate solution. The effect of the curvature of the walls on the load capacity is investigated using sinusoidal and parabolic shapes for the walls. For the case of the moving wall with a constant velocity, the leading term of its effect is proportional to the second order of the ratio of the gap to the radius. For the case of the oscillating wall, the leading term of its effect on the mean load capacity is proportional to the third order. Their proportional constants are expressed in the form of a quadratic expression of the maximum height in the cross-sectional profile of the curved wall. The effect of the curvature for the convex wall differs in magnitude from that the concave wall.
一般社団法人日本機械学会の論文
1989-10-25

同じ表面形をもつ凸面と凹面との間のしぼり膜について

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