An Analysis of the Elastic and Plastic Deformations of Machined Surfaces in Contact : 3rd Report, On the Contact of Surfaces Whose Asperities do not have Directional Qualities

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The authors have studied the elastic and plastic deformations of surface asperities in contact having directional asperities such as ground surfaces. In this report, the deformations of contacting rough surfaces whose asperities do not have directional qualities such as lapped surfaces are analyzed. The projections of asperities in contact are assumed to be circular cones. The deformations of plain joints can be obtained by synthesizing those of a conic projection with statistic of surface asperities. The theoretical results agree well with the experimental ones on lapped surfaces. The results in this report are as follows. (1) The relation between the elastic deformation or the plastic one of plain joints and the normal load is linear on a double logarithmic paper, and these deformations can be classified by the contact surface coefficient. (2) The elastic and plastic deformations in this report are 1.8 and 1.3 times those produced by the contact between a flat surface and a rough one having directional asperities respectively. (3) The increase of the contact surface coefficient K_1 produces an increase of the elastic deformation and a decrease of the plastic one, where K_1=4<tan θ>^^^-p_m/πE, p_m : plastic flow pressure, <tan θ>^^^- : mean value of tan θ when θ is half the vertical angle of projection, E : effective Young's modulus.
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